This is what a math exam looks like from 1866

Hone your math exam skills at brilliant.org/...
The Regents' questions archive: archive.org/de...
My video solving Q20 from this exam: • How to find the square...
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[@tibees]

My video solving Q20 from this exam, the square root of a decimal by hand: kzbin.info/www/bejne/pHK9p4ikjMeGbsU

[@princeharry1934]

ty

[@danielalonzocarranza4780]

Tibees give me the maps.. Like Atari... Anywuu goo d Yob.

[@danielalonzocarranza4780]

Tibees on the second exchange ill dress up a deer for a horse in majestic railway.. Be good.

[@LC-qm1xs]

Hola.. no me canso de decir eres una mujer muy preciosa. Best..

[@jeffreycloete852]

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! ..

[@jocabulous]

only 1860s kids remember

[@ThisCanBePronounced]

I learned most of this in 90s middle school. Been scouring the comments and I'm baffled I seem to be the only one.

[@JackWitaPack]

Only 3/4 of white male southerners will remember.

[@boreddude3898]

@@JackWitaPack *3/5ths of black males

[@rviiiiii]

Lol

[@tortuga7160]

jacob henke Hahah! Nice

[@anjishnu8643]

To solve this paper, one needs to be better at English than Math.

[@13ivanogre13]

"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.

[@Shaeress]

@@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.

[@jesuschrist5417]

@@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?

[@krollpeter]

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.

[@CamaradaArdi]

@@13ivanogre13 I'm non-native and I can understand the exam. It's not like we are stupid

[@aucourant9998]

Very simple mathematics. The hardest part was understanding the terminology.

[@ChonGeeSan]

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.

[@ccricers]

Even in school narrative problems weren't my strongest suit, but I was fine with the other math problems usually.

[@ChonGeeSan]

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

[@gia257]

barely hard

[@JohnJillky]

Idk if cube roots by hand is simple lol

[@jordyjordy3551]

You are such a nice and calm Person

[@davide.418]

You too

[@ttvv88]

She truly represents the Aryan ideal, Uncle Addie.

[@aashibliss2164]

ww could have been avoided if u were calm too sir

[@austrianpainterinhiding88]

So are you, father.

[@ramakrishnamishra8179]

Ok .. Adolf has commented! Thats it!

[@jerkenj3878]

In 2080 Mathematics student:I don't believe 2019 maths was like this

[@TheHadMatters]

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.

[@sanjeevtomar5651]

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.

[@lemarmaynard]

@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.

[@OXY187]

@Salvador Luna stfu

[@lukkkasz323]

@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.

[@Elijah9201]

it's weird to think that everyone who took this is dead

[@hubblebublumbubwub5215]

People who do current math exams will die too. Stay away from math exams.

[@mustafaal-ghezi1757]

Hubblebub Lumbubwub you’ve cracked the secret to eternal life

[@Elijah9201]

lol yeah

[@paulgoogol2652]

this is the mathematical proof that maths kill people.

[@nelsonbarrios1718]

*R.I.P.* to all of them ⚰️⚰️⚰️

[@bob_._.]

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.

[@Feriin]

How many gills to a hogshead? How many minum to a teaspoon?

[@bloodgain]

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.

[@douggwyn9656]

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.

[@phantomlordmxvi]

And thats why normal countrys use the metric system.

[@bob_._.]

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.]

[@rainraihan9681]

Only 90's kids remember (1890)

[@Yatukih_001]

They had advanced tech by then...

[@mikejohnstonbob935]

@@Yatukih_001 according to that time machine documentary, they had time travel back then

[@skdaroch]

damn, you are so polite. i bet, even when you curse somebody, he would say "thanks" in return.

[@Ahri_k_da]

😂

[@jihad456]

Whoever gets cursed by her would be lucky.

[@neoosedooks]

Fr

[@SaltyMeatHook]

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.

[@integza]

This is a really weird ASMR video

[@ryansager9224]

She seems like an asmr person. does she make asmrs?

[@monkidi1938]

I think she just has to be quit to not disturb other people in her house

[@bane3991]

I was just about to comment the same thing

[@VictorHCandido]

I was looking for the ASMR mention

[@hanniffydinn6019]

She needs to get on that game. Using chalk writing equations...crumbling paper, scraping pens while doing physics.

[@HalHamza]

It’s sad to know that even in the 1800s I’d have still failed maths.

[@jesuschrist5417]

Maybe in the 1800s you'd be forced to learn it more thoroughly though because they didn't have calculators.

[@HalHamza]

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.

[@Mitjitsu]

Yes, most of us would struggle to pass such papers, but people back then would struggle to do our calculator tests.

[@Keskinkilicnr1]

@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.

[@Alex-ky8bw]

yea but when you fail in the 1800s you will most likely end up homeless and hungry lol

[@AndrewDotsonvideos]

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?"

[@kevinmaldonado204]

Tell me why I can do calculus but I can't do these questions?

[@The_Revolutionist]

@@kevinmaldonado204 You simply are not used to it.

[@treyebillups8602]

Kevin Maldonado I think the notation is just really wonky.

[@liesls7]

My two favorite physics channels in one place!

[@consciouspiedy5909]

Calculus can be taught easier.

[@kazoud290]

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 !

[@Ditch901]

My God. I can only begin to imagine the calculus and physics papers of the time.

[@thoughtfox2409]

@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.

[@viktorramstrom3744]

*t e x t*

[@Andrew-jw2qs]

Australian Maths be like Oi^2 = m8, carry the roo, divide by the boomerang. The remainder is shrimps on the barbie.

[@Tombalino]

She's newzealandanise though

[@steamsteam6607]

OI

[@MsVipGirls]

Lmaooooo

[@MrCantStopTheRobot]

@@Tombalino If you divide an orc by two and carry the Hobbit, how far can King Kong throw Bilbo? Give the distance in Wetas.

[@paperpoppers]

😂

[@MultiSciGeek]

This is more of an English exam than a math exam. This looks like some Shakespeare level stuff.

[@danthemanxf]

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

[@afifassihab7953]

hhhh. xd.

[@GH-yt7eg]

@@sonacphotos You're judging this off one test, relax lol

[@TransoceanicOutreach]

@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.

[@grmpf]

"Shakespeare level stuff" How does this have 235 upvotes? I just can't…

[@PythonPlusPlus]

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%

[@Megaman99X]

The American man nuked the school the day before the test.

[@Nightceasar]

@@Megaman99X And then built a wall to keep the English, Irish, Scottish and "math" out. But then needed math to build the wall..

[@lemaildoe]

@@Nightceasar 🤣🤣🤣🤣

[@deivisony]

The Irish man drank Scotch while watching the american blow the school thinking it was a play.

[@PennyDreadful1]

Except if the Scottish man was James Clerk Maxwell. Then the exam would fail him.

[@iasimov5960]

Convert meters per second to furlongs per fortnight.

[@christianfreedom-seeker934]

😁 I took that SAME TEST in a different life and aced it! 😁 I am joking of course! 😁

[@infinitytoinfinitysquaredb7836]

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.

[@honeybadgerisme]

😁

[@kukifitte7357]

how is fortnite related to stupid maths. Anyways, dab and floss

[@prakrutisharma1234]

@@infinitytoinfinitysquaredb7836 omg wow

[@soumikd794]

Ahh the good ol times. I remember when I had to take the same exam. Time flies so fast

[@unavailableusername9694]

Lol, what side did you fight on in the Civil War?

[@paige.w17]

@@unavailableusername9694 lool

[@aromala2400]

LOL xD

[@btsgirl0909]

Congratulations for remaining alive since 1866 to the time of youtube

[@travisbickle3835]

Time flies? What are they?

[@vedantkale1163]

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.

[@ferdelance.]

EXAM 👏 REVIEW 👏

[@saadnamro878]

she kille*d it

[@lvlandfarm]

\m/

[@theviniso]

I see I'm not the only 9 year old here

[@ferdelance.]

LvlAndFarm do you know

[@lvlandfarm]

@@ferdelance. I just saw that you've got TSoP album cover and assumed you're a fan

[@joaovictorsouzadeandrade9713]

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

[@ugh6201]

I see you everywhere

[@joaovictorsouzadeandrade9713]

@@ugh6201 where r u from?

[@tomashorst9544]

Everytime I reread this comment it makes less sense

[@Captain_Nemo-y7q]

Your level of English is 'Cretin'.

[@joaovictorsouzadeandrade9713]

@@Captain_Nemo-y7q Sorry, I'm a brazilian and I don't speak very well.

[@dirkbonesteel]

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.

[@tappajaav]

M'Night Shyamalan plot twist right there

[@Gorteenminogue]

20lbs is about 9kg... I'm now looking nervously over my shoulder.

[@dacanale]

Except that is a very millennial way of thinking, to grab one’s phone and perpetrate violence upon a teacher.

[@Vapor817]

@@dacanale ok boomer

[@shechaiyah6869]

In my generation, the 1950s, we had to be able to do all this as well. Comptometers started to be used in that decade.

[@ガアラ-h3h]

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

[@vavassor]

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.

[@fabb91]

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]

That would be quite the exceptional alchemy test though, as Neptune wasn't known about until 1846 ;)

[@fabb91]

@@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....

[@knife979]

@@fabb91 LMAOOO

[@hypermangi8265]

@@knife979 Indeed.

[@kedarbahulkar189]

I did not get this. Please kindly explain. Thanks

[@alicewonderland7218]

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!

[@pythor2]

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. :)

[@heliumphoenix]

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)

[@bloodgain]

I'm saving this to use as a double-trick question: "Which weighs more, a pound of gold or a pound of feathers?"

[@WorBlux]

Probably more like troy ounces vs stones or hundredweights.

[@thedillestpickle]

...metric system Get with the program

[@quantum7401]

Damn trick question got me.

[@Albukhshi]

@@WorBlux Not necessarily. What matters is that you know that the troy ounces are smaller than Avoirdupois ones.

[@quahntasy]

Only 19th century kids will remember this. What fun times they were, go to war and come back home to do some math problems.

[@zikomo8913]

@@46pi26 and then go to the doctor. the good doctor.

[@46pi26]

@@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.

[@nossasenhoradoo871]

"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".

[@singhmandeep8695]

@@nossasenhoradoo871 visit a doctor as soon as possible

[@nossasenhoradoo871]

"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.

[@gandalfthethotful479]

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 ;)

[@joshuakimmich4486]

No wonder people became criminals and robbed others in hopes they could gather enough *money* and go to Tahiti.

[@stirnermax2396]

Its a magical place

[@ravenaxyz]

@@stirnermax2396 30 mins late, damn!

[@PanglossDr]

like they do today?

[@rybread5718]

Alright Dutch.

[@stirnermax2396]

@@ravenaxyz xD

[@kuraddohikari]

I grew up in New York and we still have Regents exams, but yeah they're in geometry, trigonometry, pre-calculus

[@user-ok8yq6nc6x]

And other subjects

[@tonyv2819]

And they wonder why Tom Sawyer went rogue painting all those fences...!

[@THREA]

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!

[@davidfletcher4952]

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?

[@davidfletcher4952]

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! :)

[@robertlozyniak3661]

There is a video on KZbin 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!

[@THREA]

@@robertlozyniak3661 i will go and check it out!

[@carlrey8015]

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 :)

[@OMGclueless]

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.

[@JivanPal]

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.

[@thanksforthefish42]

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.

[@Lunaskyuwu]

thanksforthefish42 looks like tok much effort

[@zupythenoob]

Thanks for the explanation! Got the 3 but didn't catch the 7.

[@mzallocc]

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.

[@chickensdone1]

@@mzallocc that is how I solved the problem, too. Good stuff!

[@lovfro]

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.

[@janmam6927]

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

[@acidtabi]

as a recent graduate from a public school in New York, the regents exams are still alive and well

[@AnonimityAssured]

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.

[@tibees]

Lol oops

[@csbruce]

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.

[@tychocurious]

i live in new york.... can confirm we STILL have these regents exams to this day.................

[@Shane-zo4mg]

It's so funny to hear math professionals still refusing to say the word multiply.

[@manictiger]

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.

[@schrodingerscat3912]

...so how about the product?

[@zupythenoob]

10/10 for effort Well done

[@Mcpwnt]

Maybe Parthenogenesis

[@Loraguy]

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 :-)

[@arthurcab]

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.

[@hypeedits558]

“Old school” *I see what you did there*

[@RonBertrand]

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.

[@KnowingBetter]

This question has me a little bit shook. SHOOK.

[@martingoldblunt5163]

You lied on your 4k video.

[@GlennTheSadMarinersFan]

I wonder if this was recommended because I subscribed to you .

[@aglassofmilk5779]

Knowing Better ok

[@Lunaskyuwu]

this feels like asmr

[@drunkenmasterii3250]

It is if you have a thing for private teachers.

[@mrkillums8219]

Its because it is.

[@misatoblushing6913]

this meme should die

[@BrightBlueJim]

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.

[@alexseguin5245]

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.

[@drm9694]

I live in New York and we still use regents exams. The current math exams we have are algebra 1, geometry, and algebra 2.

[@anymaths]

my videos will help for your exam.

[@rachelkrats5569]

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

[@drm9694]

@@rachelkrats5569 I actually just moved to New York from Ohio less than two years ago.

[@justindorsheimer4857]

9:44 "excuse me? um...." Lmao

[@hbm293]

389017 == 73^3 here's the answer :P (obtained by clever trial & error...)

[@trideepbiswas]

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.

[@sofiakgabriel]

Just watching it gave me anxiety

[@stevethecatcouch6532]

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.

[@sum6198]

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

[@brunileshi]

Q17: cube root of 389 017. The cube root is smaller than 100. The last digit is 7, thus the last digit of the root must be 3, because (x*10 + 3) = 27 + something that ends with a zero. Now we check the second last digit using (a+b)^3 = a^3 + 3a^2 b + 3 a b^2 + b^3. The second last digit corresponds to 3 x 9 + 2 and must be 1. Thus, x equals 7. Answer = 73.

[@zachthompson1494]

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. :)

[@RichFreeman]

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.

[@Volvoman90]

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]

And i thought retarded units were a hassle today, i feel bad for those who didn't use metric system back in the day.

[@Volvoman90]

@@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]

So, basically, this is why people came up with the metric system.

[@Feriin]

@@MaciejBogdanStepien Yeah, they found out that a lot of people are just stupid can can't grasp base 12 or base 60 measurements.

[@WorBlux]

@@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.

[@hanniffydinn6019]

Honestly I think why I watch is because this is virtually an ASMR channel for geeks.

[@uruiamnot]

Nah, you like blondes.

[@tracepillar8382]

@@uruiamnot lol'd

[@kingofthejungle3833]

Q.5 a pk might be a something such as a wool pack, a bushel was a volumetric measure (which I think was equal to 8 gallons) and pint was roughly equal to 1 litre. Q.7 cotton was sold (and still is on futures exchanges) by the bushel, and gold by the ounce Q.9 you actually multiply 60x24x7 then divide the result by your 8 and a half million, otherwise it would get too messy Q.17 they'd have used a slide rule

[@bryan31385]

#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.

[@patpatterson9269]

I find your videos fun. I actually went to school in Utica 1945 - 1952

[@JivanPal]

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.

[@NorthDownReader]

'Where you are reading "8/4", it is actually printed as "3/4",' An earlier question too, not just #22

[@KhAnubis]

This is great, it's like a math lesson and a history lesson all in one!

[@wizardsuth]

Question 10 quotient: 9 divisor: 3 ) 29 : dividend - 27 remainder: 2 29 / 3 = 9 2/3. The common fraction 2/3 is obtained by dividing the remainder by the divisor.

[@davidbrogan606]

For question 5, a bushel contains 4 pecks, a peck contains 8 dry quarts. So convert to quarts divide by 12 and I think it comes out to 5 bu. 1 pk. 6 qt. 8 oz.

[@Salsuero]

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.

[@wongpakyin4860]

3 8/4 would be 5 it’s definitely an 8 in the exam

[@stuffedpotato9826]

@@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??

[@st0ox]

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^^

[@gianfrancostefanoli7854]

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

[@almostoneword]

@@gianfrancostefanoli7854 Ha! No.

[@alenvaneci]

@@gianfrancostefanoli7854 It's not the language that changed a lot, it's the conventional script it is written in.

[@erkinalp]

@@alenvaneci Fraktur was a font for Latin script, just weirdly ligatured.

[@KerimWirthSuperLps]

Es ist wirklich nicht schwierig, die Schrift zu lesen. Man muss sich wirklich nur kurz daran gewöhnen.

[@barrymcockener4336]

When I was in high school the regents exams were very much alive.

[@dapsapsrp]

Potash were somewhat of a broad term used to describe or label mined salts that contained potassium and were used in agricultural fertilizer. Very common in the US back then. They were water soluble and made for an easy way to permeate fertilizers into soil. Cwt was used for commodities trading and pricing in N. America, mostly the US, to describe hundred weight of something usually in pounds. The Latin "C", for 100, was a simple way to abbreviate it. Not used much anymore and pounds and Imperial tons are very, very slowly becoming replaced with metric. This is as much of a logic and problem solving test as it is a mathematics test.

[@captainjohnh9405]

I think for number 7 (cotton and gold dust) the units for cotton would be either pounds or hundred weight (100 lbs.) and troy ounces for gold dust. Number 15: tons is short tons (2000 lbs.), I THINK qr. is a "large sack" (224 lbs). In 16 the "M" is mill, as we use "K" today to represent 1000, Also, a board foot of wood is defined as 12 inches x 12 inches x 1 inch thick.

[@SunriseFireberry]

math is math, no matter the century, rigorous, demanding, deterministic

[@buttup8148]

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.

[@2kreskimatmy]

Definitely not. Math is not THAT universal as you can think

[@Saidor570]

@@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]

@@Saidor570 but the complex numbers were ''invented'' just in Gauss Age...

[@Saidor570]

@@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 :)

[@noriakikakyoin6009]

youtube's recommendation algorithm is so weird 🤨

[@deepdownyt]

True, I never searched anything math related before. And now of course my recommendations is full of math, chess and physics video...

[@-overdooo-]

M3rk fan?

[@09simid]

Some unintended ASMR is going on here! Listening to you explaining this is just so calming!

[@ENAIRAMA1]

The question about the partial product is specifically for that way. You did the regrouping method. Children in 4th grade in the State of New York learn the partial product, expanded notation, regrouping and area product methods. When you multiply with more than one digit with partial product the method is as follow: For example 12 by 28; (20x10)+(20x2)+(8x10)+(8x2)=200+40+80+16=200+120+16=336. I am not a teacher, I help my child with these problems all the time. I learned them myself, since I never knew the other methods. Before was the regrouping method and that was it.

[@pbierre]

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.)

[@MeFreeBee]

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

[@MKD1101]

*She definitely works out!*

[@SNOUPS4]

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.

[@PaulSteMarie]

This is all very straightforward arithmetic as used in commerce. #16 is an invoice for lumber, which is still measured in board feet, which is roughly 1/12 of a cubic foot. The M probably stands for thousands. #18 is an interest calculation. Presumably interest rates at the time were fixed by law, but they are asking for the present value of a future cash flow.

[@Perryman1138]

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!

[@waverleyrocker]

You should do asmr videos. You'd make bank.

[@iceberg789]

math asmr ?

[@vinzer72frie]

there's some girl that does asmr with C programs I forgot her name

[@ENZOxDV9]

@Alchemica Blackwood she'd make even more bank getting rammed by 2 dongs but not everybody wants to do that!

[@wilhelmu]

@@ENZOxDV9 actually no, good asmr gets hundreds of thousands of views, millions sometimes. pornhub videos are quickly forgotten, as are countless camsessions

[@martinramirezjr7872]

@@iceberg789 That would definitely increase the flux over my cylindrical surface.

[@sammosaurusrex]

As a New Yorker, I can confirm we still take Regents exams, but they're much more modern

[@pbierre]

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.

[@jjonh6419]

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'

[@24kGoldenRocket]

Answer for Q7....Same units as would be used today. Gold is weighed in Pennyweights, Troy Ounces or Troy Pounds. Cotton is weighed in Pounds and Ounces avoirdupois...same as the weight measure used at your local grocer in the UK and USA

[@schr4nz]

Arithmetic is important but it's not important for people to use it fluently, you just have to understand the concepts and not necessarily be well practiced in using it, but it does come in handy if you do need it... In the outlier scenario where you don't have your smart phone... Interesting looking back though, thanks 😊

[@BigGreekCock]

Nigga, if you think arithmetics aren't important, then try baking a cake without the exact measures

[@stevethecatcouch6532]

In 1866 you had to be well practiced at doing it.

[@schr4nz]

​@@stevethecatcouch6532 I don't disagree: it was 1866 - for clarity, I was replying to her remark toward the end of the video about whether it's a good or bad thing that people in advanced fields often have to use smartphones etc with basic things like bill splitting, my answer is no, I don't see that as a problem

[@stevethecatcouch6532]

@@schr4nz I missed the context. I agree, on a day to day basis, it makes sense to let a machine do the grunt work.

[@medexamtoolscom]

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.

[@okaro6595]

You solved a wrong problem. It was 389017, not 889017.

[@romaa3985]

the youtube search algorithms are mathematically 1000x more complex than this test.

[@debrajean9432]

Question #7. Gold is weighed differently than everything else. An ounce of gold is measured by troy weights, and the avoirdupois ounce is used for commodities, like cotton. There are 28.35 grams in a troy ounce, and 31.1 grams in an avoirdupois ounce.

[@Grundini91]

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.

[@gregsimpson9391]

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.

[@video99couk]

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?

[@dedalus0122]

I'd say every time she said 8/4, it was really 3/4.

[@nandans2506]

Good old days when maths was about numbers

[@nossasenhoradoo871]

"Good old days when maths was about numbers" It still is. Except that now all national debts are in trillions!

[@KingOfHearts901]

GuruNandan, I think the joke may have flown over a few people's heads.

[@Merrid67play]

Gold is measured in Troy weight (14oz to the pound), and cotton in avoirdupois (16oz to the pound)

[@rdbchase]

The answer to #3 is "in the place corresponding to that of the digit from the second multiplicand from which the partial product is formed".

[@bradbilbo6696]

HI, The 8/4 you keep seeing are really 3/4. The three is in a font that almost closes.

[@daveseddon5227]

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!

[@The_Revolutionist]

Our teacher showed us some of these old tools! My father also used these.

[@treyebillups8602]

Jeez, that must have been tedious. I'm so thankful that our calculators can do logs now

[@khushipandey2482]

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😅😅😅😅

[@robertlozyniak3661]

@@khushipandey2482 Are you allowed to use an abacus?

[@robertlozyniak3661]

@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.)

[@Ghaffar_KH]

Ah the good old Regents' Questions. I remember failing in those as I have been too busy impressing the ladies with my Cattleman Revolver rather than studying.

[@Moley1Moleo]

Question 18 seems to be a financial question, regarding the concept of 'discounting' which is that promises of something in the future are worth a bit less than getting that thing now. For instance, if I promised you $1million a year form now instead of today, you might complain that: * You want to spend it now on goods/services you desperately need. * That money will be worth a bit less due to inflation after a year's time. * You could invest in business/shares/savings and you are missing out on a year's worth of profit/dividends/interest. And therefore $1million today is worth much more to you than $1million a year from now. The question seems to assume some known discounting rate, which might have been somewhat standard at the time (or perhaps it is standard to discount according to inflation or some other commonly published figure).

[@RichFreeman]

Agree. In fact I think most would struggle with a problem of this nature even today even given the discount rate. My guess is that there was some kind of standard that rural banks employed when dealing with the general public, and that no doubt it was set such that the banks would be quite happy to buy those notes. Who cares whether the rates in NYC are 5% or 6% when you can just charge the farmer 15%. It does strike me as interesting that buying a note like this would be something a normal person might be concerned with. I guess in a town where everybody knows everybody else I can just scribble an IOU on a napkin and the local bank can convert it to gold dust and treat it as a bearer bond...

[@mfkman]

the cube root I found fairly quickly. First: cubed root of 10^6 is 10^2, so needs to be less than 100, 2 digits. Because the number ends in 7, the cubed root must end in 3. Half way: 50^3 is 125000, much too low. So try somewhere inbetween 70^3 is 343000, fairly close, so as we said it must end in 3, so try 73 - and yes, that is the answer