Dear High School (and College) Students, STOP Making These Math Errors
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No regrets making this video, the comments are too good. But for those who find these way too easy (yes I know it's not an advanced video at all), this recent one I did on imaginary numbers may be more to your liking.
The Real World Uses of Imaginary Numbers: th-cam.com/video/_h49ilnTmW4/w-d-xo.html
Very useful video, I understood everything, but I always messed up in the 4th point. Thank you!
You listed all the mistakkes that I made thanks for correcting me! You made my day☺️.
What is the modulus of -x?
Hey MajorPrep please do more videos like this! I love how you demonstrate exactly whats wrong, and point people in the proper direction. Its a quick overview but thats part of what makes it great. Please do more videos connecting mathematics to programming ;).
I tried to find a playlist for this kind of stuff, but you dont seem to have one sadly.
I find it interesting that most of these were repeated to no end up to the point and if you would ask someone what type of error would be proof that you didn't pay any attention most of these would have made the list.
The ones I can understand is forgetting brackets if you use a calculator and so on since that does happen to me on a somewhat regular basis (usually only one though and at some point I started to ignore - if it's just multiplications and arrive at the correct sign in my head since it is simply faster).
Also one mistake which didn't make the list and which I do all the time and also see so often it's more of a surprise if it does not appear is forgetting the +c when integrating.
I mean I know it's there and all I just rarely write it down.
Making simple algebra mistakes in a complex calculus problem is the most frustrating thing
Oh my gosh seriously!
Absolutely! I remember that when we did matrices in the advanced math class, calculating determinants for anything beyond 5x5 (with simple numbers) was ridiculously difficult because you're bound to do simple mistakes somewhere and the answer is different every time! 😛
I think I wanted to calculate the determinant of a 10x10 matrix just to challenge myself (or I might have done it to distract myself in a boring history class) and I finally gave it up because I had a different result pretty much every time. And I'm good at math!
@@jensraab2902 No, Jens. You're bad at math.
-6 - 2 yep, that's -4, why aren't I able to simplify this derivative, what am I missing!?
Making addition or multiplication errors because you're going to fast.
When u gotta put 1+1 on a calculator JUST to make sure
It's 3
Its 4. Use your fingers. You have to trust in yourself.
And still got wrong answer
1 >>> 1 finger
+ >>> 2 fingers
1 >>> 1 finger
Count carefully in case you miss any fingers
@@amaikoori Thank you for the reminder.Appreciate it
As someone who grew up with bad math fundamentals, these mistakes are extremely relatable. It took me a while to realize I should be more humble and actually study basic math.
Where should a sophomorer start
@@user-rd6bc2wo6r hire a tutor I recommend
Just 3 years ago.... I was so bad at mathematics... I even got an 'F' in my subject & I don't even know how to do these kindergarten stuffs. After that 'F', I worked hard day & night, tried to get all of mathematical rules & geometric formulas theorems, after that 4 months when another test was taken, I triumphantly scored 98/100 & the highest of Math class in my school. That day, I was the happiest to none, it just takes a dedication & inspiration to do better..
Any tips or recommended resources?
yeah from where did you learn all the rules?
@@totallegend2480 Organic Chemistry Tutor and PatrickJMT
Congrats! That's a massive inspiration
How much work did you put in studying everyday?
Forgetting +C after the indefinite integral
hit me like a truck
Those little shits keep me up all night
Or thinking there's a difference between +c or -c
I had a professor make us put "unit^2" ...
@@MrGiraffeify Well it's true
I swear that the biggest math mistake for me is probably misreading the question and somehow turning i into 1.
Lol
I do that too, except it's due to my own bad handwriting (like I will confuse my own 4s for 9s, or my 7s for 1s)
@@kelvinubaechu 🤣same to u
There are times where I lose marks for not seeing that negative sign in front of the equation instead of as a subtraction.
I also confuse some teachers with my handwriting when I write my 5s (because they look like 6) or 7s (because they look like 1s).
Hahaha i = square root of -1
Math is like a new language, keep practicing and you'll be fluent. It will become easier trust me
thanks creed
Thanks creed
Thanks creed
Thanks creed (I don't know how you are though)
No
That awkward moment when...
You forget the +C in an indefinite integral
You forget the negative root of a square or any even power
You square an expression early on but still give the negative answer
You give negative answers to questions on absolute values when the question said 'positive integers'
You convert a logarithm to a base but then later on convert it back
You forget that the definite integral of 1/x from -1 to 1 is undefined
You are reading this comment instead of studying for your paper tomorrow
integral of 1/x on [-1;1] is = to 0
@@Rzko No. If you haven't studied enough calculus, you can understand it as the natural log of a negative number is undefined
@@user-bk5jr4du1s watch the video of black pen red pen about it
@@Rzko I'm sorry for making a mistake of forgetting the absolute value sign from the integral of 1/x. But still, if you integrate 1/x from -1 to 1, you'll get -infinity + infinity, which doesn't tell you anything, it could be either divergent or convergent and you have no way to tell. This is a problem of the ways we defined things in calculus, not some fundamental truth about the universe or something.
@@user-bk5jr4du1s Nope because there is exactly the same quantity at the left of the y axis than at the right. Again if you are interested about this watch the video of bprd about this or search it on internet on online integral calculus
x^2=4
Forgetting the negative result.
Did it once *what a shame*
OnlyMyRailgun Unknown my exam was tday and some people forgot the plus minus as well
x^2 = -4
???
*i* dont know..
@@maxsimes Ok here is the door pls leave
@@maxsimes x^2=4
=> x1=2, x2=-2
that what he meant
"Hey I'm bad at math and I can prove it"
Directly or by contradiction? Please show all work to receive full credit.
I see u like pure math :3
lollll, "nahhh i shall use my deduction skillzzz to prove!"
That is the best comment!
The first thing my Discrete Math teacher ever told us: “Generally, you’ll solve by contradiction. Abductive reasoning takes too long and inductive reasoning takes longer than solving by contradiction.”
Lmao, spot on
I stumbled on this randomly and I'm like holy shit there used to be a time when actual numbers appeared in my math problems lmao
I tell everyone that high level maths is like eating alphabet soup and finding a number.
Especially when you start getting into doing derivatives the slow way…
The government elites are taking away our God given numbers, and replacing it with this these letters and imaginary crazy talk 😰😰😢🇺🇲🇺🇲
@@honkhonk8009 very SAD...!!!11!
Finally, a math video that doesn't make me feel stupid.
I love how done you sound in this video. I can practically hear your cries of distress from your tutoring years
"No, that doesn't work like... this... no, that's not how it's done, you can't just... no please stop - oh goddammit"
Finally someone gets it
I can hear Gordon Ramsay in this comment.
bwahahahaha
I guess that's where tutoring people in their mid 20s that still don't know how PEDMAS works gets ya.
But these are not that hard
Just remember these things while doing Maths.
- Do questions neatly
- Do questions patiently
- Try not to skip major steps( like not doing them in the head)
- Don't be lazy while doing question( Try not to make solution as short you can)
And this will increase your chances to get correct answer in the first try.
These work for me. And remember don't be lazy, tell this to yourself while solving problems.
Unless your teacher gave a time limit
- be confident
-Cry while questioning major life decisions.
-End up with an identity.
-Realise you forgot to multiply with a minus sign somewhere.
-Cry harder.
These won't work for me but I do them anyways.
Dhanyavad. I'll get back to solving Kreyszig now.
Engineering admission in bangladesh gives small space so its discouraged to make it long asf
Math teacher here: This video is so accurate that I feel like I'm grading student's exams at this very moment. Not a good feeling.
im sorry for your loss
I'm coming back to this video 3 years after seeing it for the first time and wow, everything seems really basic now, which probably means I improved a lot, but it really helped me back when I first watched it. Thank you for making this, these simple foundations are essential for those struggling before they can really learn to enjoy Math.
bruh i'm watching this and it does NOT seem basic to me lol
@@sabutp35 it will soon if you try hard enough
"I’m bad at math... and I can prove it" 🤣😂
pi=2
now wheres my medal!
If you are bad at maths.... How can you PROVE anything.😁😁😁
@@Blox117 I don't see anything wrong with this.
It's a simple equation and the answer is p = 2/i 😛
"... And I can prove it mathematically"
666 likes satan confirm
>During courses: this
>On exams: "Calculate an elliptical integral of second class."
@@gytoser801 So... you're saying... it *does* have solutions?
Here I am trying to wrap my head around covariant, contravariant, christawfull, tensor calculus and topology. Then I come across "elliptical integral" and I don't even know WTF that is.
In class: Perimeter of a circle
On the test: Perimeter of an ellipse
@@death_parade it's like an Integral, except elliptical
I never learnt that "keep it, change it, flip it" its so simple, yet it changes everything, thankyou! xD Excellent video, I think people get caught up in degrees like engineering doing the advanced calculus/physics courses, that they often forget the basics when it comes to maths and end up tripping themselves up on simple topics
This reminds me of the day I, as a 8th grade student, understood the explanation of the binomial formulas better than the teacher explaining them to me. We had a long discussion, she called some other students to correct my "mistake" and two weeks later she had to admit she was wrong... I really hate the fact she didn't even acknowledge that her entire campaign against me was completely out of place or even that i was right all along.
At least she stated she was wrong.
Bro i had a similar situation (11th grade) in chemistry.
It was about a simple temperature increasing if the volume increases.
Basic but the teacher made the class question what i said and ultimately said i was wrong.
Lol.
that actually sounds epic lol, what example did you use to prove her wrong? (If you can remember at this point)
The ego in the comment section is glorious
Whomst've doth calculus like me sincr 6th grade ?
Mohammed jawahri learn how to type.
The Shocking woooosh
"I learned this when I was in 1st grade!"
goes well with the ego in the original video then...
I like how many people commented on this video about other commenter’s egos, just to inflate their own egos and point out how humble and perfect they are because they’d *never* do such a thing.
I don’t know what that says about me, commenting on their comments on other people’s comments, but lets just assume I have some really messed up ego issues and move on.
Nothing But The Austin Meta ego
😂👏👏👏 What a comment!
I guess everybody is proud of their hard work, observations, etc. Can't blame them. Really underrated comment as I could not find a single egoistic calc nerd, just "humble" humans.
Inception all over again
If you come up with any way to fu*k up math there is a 101% chance I have done it before.
I especially agree with the last bit. Don’t memorise method, memorise what it means, then “just figure out” the method
Another smart thing you can always do when dealing with algebra is simply putting in the numbers instead of the letters when you think you have the solution and check "did i actually do it right?" and if you do that you should technically never be wrong unless you do something wrong in your checking :) Have a great day and thanks for reading everyone who is reading this!
So basically substitution? ^^
You know what suprises me the most... Eventhough I have use the same calculator for almost 3 years, there are still some more formulas, or hidden methods, or something that is in the calculator that I still don't know of...
Azizul Adnan lmao ikr😂
TIs can calculate derivatives, integrals, and a bunch of statistics related things. Also you can program it to have flappy bird
DON'T use calculators. Learn to do all basic operations by hand. You can't learn the structure of numbers or what they mean if you rely on calculators as a crutch.
@@SerbAtheist i spent a whole year doing that and i dont regret one bit buying one
@@SerbAtheist can't do that in tests though.
Spend ten seconds doing it by hand or two plugging it into a calculator?
You need these time saves.
Why did I watch this video in full?
Why did I scroll through the comments for so long afterwards?
Why am I now making a comment?
Why do I exist?
Jacob Goodman Omg, this is literally the most relatable thing I’ve seen in all of 2019
Why did I read this whole comment?
Why am I commenting on it?
Why am I doing this 8 months after?
Why do I think doing this is at all clever?
Relatable
Got so deep in a sec
Go watch exurb1a
Yes, Yes, YES... It had happened to me before. Focusing in lots of rules has made me forgotten what math really is. The rules are just a summary. Maths is the language of how reality works.
Omg I'm so bad at math and I felt so called out in this video, but I can't thank you enough for doing it because I've understood so many things that in class I was not able to fit in my head. THANK YOU SO MUCH!
7:37 - Dividing by x isn' technically wrong, but you have to specify that you're assuming that x isn't 0 and you're essentially giving up on a possible solution which you must specify later (x=0).
If it is an equation of x^2/x=1 then you cannot have 0 as a solution for that case since it will be indefinite if it is plugged
I was just going to comment this.
Exactly, they're the same value. You can device them as long as the × does not equal zero. I don't understand why he said that we can't
If you're dividing by x, you have to take care of the case x = 0 separately first before you can continue with the case where x = 0, otherwise the video is spot on.
@@tasneemahmed5821 Because doing that is bad, unmathematical practice, and not something you see mathematicians do, so there is no reason to advocate for that. Just do it the way mathematicians do it. Problem solved. It ain't that hard to follow.
1. Multiplying binomials
2. Simplifying expressions inside radicals
3. Absolute values
4. Simplifying rational expressions
5. Complex fractions
6. Setting up quadratic equations
7. Using parentheses on your calculator
Bentley Ghioda I did all of those on algebra 1
The one I didn't think about the most is the absolute value
but what does x mean??? is there treasure buried there! :D
You mean polynomials right?
Well, more in a more generalized way, yes. The concept carries to longer polynomials but the video covered binomial multiplication.
This is such a great video. I've been pretty lousy at maths all my life, and recently I've been working with a tutor because I want to go to a college that needs you to pass a higher math test (like SATs but a Croatian version I guess). These are ALL the mistakes I made and had to unlearn. After I learned the proper way to solve these problems, math has gotten so much easier!
That last part reminded me of a Tom Lehrer quote. "The important thing is to understand what you're doing, rather than to get the right answer."
I'm a high school math teacher, and I see these mistakes ALL THE TIME! You're feeling my pain, bro!
The worst is when I know I've harped on these things several times in a short interval of time and see absolutely no decrease in these mistakes!
as a sophmore i can tell you that really dont like simeltenous and quadratic equations
I walk on mental crutches solving 12/x=6 by multiplying by x and dividing by 6. I learn to “walk” as I try to teach my kids in elementary school to skip crutches. Are we still training kids to follow rules and mnemonics without building _intuitive_ understanding and feel for these rules? I asked adults including PhDs, why pemdas? Like me no one ever thought why, “they told me so”, “convention”, while it’s common sense if we recall that multiplication is repeated addition. I helped 7 y.o. figure out herself that 19 x 3 = 20 x 3 - 1 x 3, so hopefully a (b+c) = ab+ac in middle school will be common sense. Before they learned long division I came up with the idea that you share whatever number of candies you want in the first go, and then attempt to share the rest. But it’s hard to reinvent the wheel. Will appreciate any links to building intuitive understanding.
@@ltpetrenko you sound like the math teacher everyone on the planet needs
@@ltpetrenko Montessori schools use all physical tools to demonstrate basic arithmetic operations.
@@ltpetrenko dayum i wish i had you as a teacher
I’m in calculus and I make these kind of mistakes. Getting better, but this was helpful because it has ALL the common ones together
lol seriously?
Samuel Carlson Wow, for real?
theFizzyGaming there’s a difference between a brain fart and habitually making an error. It it happens once then you get the test back, smack your forehead and go “doh! That was silly”. But if you regularly make that error, it shows that you lack some fundamental knowledge that you should have, and “math rules” won’t teach you that knowledge.
@@tamircohen1512 lOl SeRiOuSlY¿
@@williamplay1000 WoW, fOr ReAl¿
Practice, practice, practice - even saying out loud what you are doing can help, showing each step helps. I often see people doing the math in their head silently. Doing that before fully grasping each step can cause errors and make it hard to solve problems. When stuck, I often start by doing each step written out fully - nothing to chance. thx
Man, I forgot what it was like learning this stuff for the first time. It's all second nature and I do it in my head, but I remember having to reason my way through it back in the day.
Its so true what he said at the end, everyone just memorizes formulas and rules that they just don't know what they are doing. I have always tried to stay away from memorizing anything and most of the time I just try to understand the concepts and it has just become second nature to me. The best thing for math is don't memorize but try understand the concepts.
Bilal Memon the problem is thats how its taught, for some reason, but like physics is taught intuitively like hey guys lets figure out why we say there is a fictitous force opposite to linear acceleration due to differing inertial reference frames, in a way that makes u understand w h y that is and can make sense of where it comes from instead of accepting it like magic and completely missing the point of education like maths does a lot
The big problem is that most teachers don't tell you WHY it works, they just say it works.
Sigh... Miss you Mister Jonathan. You were the only good math teacher I had...
ki kus No there are teachers who explain why and those who dont thats mutually exclusive
@ki kus I mean, sometimes that's true, but I've certainly seen teachers that are like "just do it it works and even though I'm a math major I also don't know how it works so there do it"
The most annoying thing is watching people complain about how many formulas they have to memorize for physics, when all they're actually memorizing is 30 different rearrangements and substitutions of 5 actual formulas.
As someone who enjoys math and has taken AP Precalc and is soon gonna take AP Calc next semester, these are very good tips. Tips that I grew up learning through trial and error over my early high school years. While math may be difficult to a lot of people at first, the BEST advice I would give is PRACTICE! Math is learned through a process of trial and error and repetition. The more you do it, the easier it’ll get.
Back in high school, i had a rational function quiz. I accidentally did the cancellation of terms that did not actually cancel and got a D on it...
Can you do a video of stupid mistakes in calculus? Like the algebra concepts everyone forgot about, formulas everyone forgot about, proofs errors, etc.
- Someone in AP calculus who needs help.
++++1
yeah, most people who watches MajorPrep are in calc courses or Differential Equations, physics or something else; not anymore in linear algebra courses BUT, Guys, Please, drop the Ego: Admit that sometimes we make mistakes. I have made these mistakes, more than I wish to admit. Hell I did one of these in the final of calculus III last year. Saved me that my teacher got my stupid mistake and just pointed at it in the test but did not rest me points for it, and he could... he should actually. I messed it up big time.
Yeah, seriously. The reaction from some of the comments come off as condescending and makes the channel feels unwelcoming to those who are new to engineering (me, for example) or anybody who wants to get into math.
I really have made this mistakes in past and mistakes should be corrected and should not be kept hidden...
This isn’t linear algebra?
Wtf, quadratic equations aren't linear algebra
i never made these mistakes.
I have never felt so exposed, torn apart and rebuilt in my life💀
These are absolutely useful and yeah, everything on this video is explained very clearly even though some topics covered here are already teached on my school. Great video for refreshing your mind to avoid making mistakes like these ever again. Keep it up. You're a lifesaver man. 👍
I remember when I was in algebra 2 in high school, a lot of my fellow students had these issues. Unfortunately a lot of these students were dismissed by math teachers as being lazy and not wanting to do the work. Though some of the kids just wanted the easy way, plenty of kids were struggling with basics like this because they were thinking of math as memorization of rules instead of what was actually happening with the numbers and functions
I can't believe I got all the way to Calculus III without realizing that. Math is basically a set of rules/propositions/theorems that guide you to solving different types of problems, not a step-by-step procedure on getting the right answer. It took a F and a D- on the first two exams for me to realize that.
how about how these teachers keep doing memory tests as if thats what mathematics is?
or somehow arithmetic errors somehow disprove your understanding of concepts?
To be fair you can only get an understanding of how functions work once you understand the rules and can play around with them.
Our math teacher used to give us a song for every new topic and to this day I havent forgot what I studied in grade 10 & 11 & 12
Now that's what I call a teacher!
share some of those
That's awesome tbh
I like how my teacher already prevented these errors from happening! Clearly the best math teacher I had.
Thanks to my math teachers and my awareness ☺️ I almost never did these mistakes
same
Watching maths at 4am, everything is ok
lamoo, ive been wathcing math since 3am instead of doin hw😂
SAME I-
Ahahah the clock just hit 4(am) for me
This gets brushed over in school. I'm now in calc and and I still make these mistakes. Instead of showing us how to read word problems half the time, they should of taught us how the simple math works.
You're in calculus, you know how math works. Its called slowing down and checking your work, making sure you're operating within the mathematical constraints and remembering the rules.
"keep, change, flip"
yea, we call that *ReCipROcAl* here in my country!
I needed this! I REALLY needed this! Thank you for saving my life.
This helped me so much it’s ridiculous. I was never somebody who could learn math easily so when I was put into an advanced course I couldn’t catch up with the rest of the class and ALWAYS missed the small details. Watching this now made everything make MUCH more sense because all of my teachers always told me when I did a problem wrong but never really told me WHY I did, they just repeated a bunch of steps and expected me to just get it on my own. Any who, I know to a lot of people in this comment section these are really easy mistakes but to people who aren’t the best at math like myself we really needed it 😂
"yeah, that's completely wrong " xD I don't know why that sounded so sassy xD
I don't make silly mistakes in algebra.
But I do make silly mistakes in numbers like 17+25 which is frustrating.
The way I remember 2:51 is that if x (or interger) can't be factored out by both expressions, then there's nothing you can cancel out.
I remember this mistake was huge in trig for a lot of my classmates. I guess the introduction of trig functions made it confusing to look at.
I totally agree, there are a lot of high schoolers that make these mistakes. Another thing I would totally add to this list is trigonometric functions. People have all these absurd ideas about notation, graphing them, memory aids... that just really muddy the waters, instead of treating them like any other function. There are much better ways to teach those concepts rather than relying on memory aids that students forget from year to year.
I ALMOST added trig stuff to the video cause I see people have like sinx=.5 and they’ll sometimes try to divide both sides by sin which is just painful to see.
We're humans. We do mistakes
For whatever reason the way trigonometry is taught in school is complete ass, which is terrible because it’s the single most important area in math for learning physics.
SOH CAH TOA
My problem is throwing sin (π) in the calculador in degree mode
I was just thinking, if your calculator gives you a negative number when you square a negative number, well, I was thinking 'Get a new calculator!' .. then I checked what my calculator does and now I'm getting a new calculator
"Getting lost in the rules you forget what you're doing"
Truer words have never been spoken
You cleared my doubt that I had from last 4-5 years. Thank you
Wtf is the box method for factoring
A method I hate but I have worked with students who only learned it that way.
MajorPrep Shoutout to Kumon.
@@shaunakkulkarni4679 I knew the quadratic formula before I know how to factor 😂. And even worse, I am in a Secondary Maths Olympiad team.
r/iamverysmart
I didn't know that that even exist, I only cross-multiplications and quadratic formula for binomials lol
I love the title when it says '' Dear high school (and college) students''
A common mistake I see is canceling out numbers or variables inside trigonometric functions with the denominator :
sin(2x)/2 they cancel out the 2, or if it is sin(2x)/x they cancel out the x.
You are only allowed to cancel a number or variable if it is inside the trigonometric function:
sin(x*2/x) you can cancel out the x and you are left with sin(2).
This rule also applies to other trigonometric functions.
I love this message. These mistakes are the reason why I go back through math from Geometry every year.
Excellent video! I think a large part of the problem is that often 'teaching' consists of telling students rules they can follow that helps them make it look like they know what they're doing. This becomes reinforced due to a fundamental limitation of testing, namely, we can measure only what we can see. As such, understanding is largely inferred. Unfortunately, tests often can't really tell the difference between looking like you know what you are doing, and actually understanding what you are doing.
Yeah cus they know they understand the rules, but they dont apply them in the way they should be applied. Or, at least they dont realize which rule counts in that scenario.
What are these comments. r/Iamverysmart material everywhere
This happens in pretty much every youtube video related to math, just need to accept it lol
To be honest I've never seen people doing this mistakes in high school. And it wasn't even a scientific high school.
r/iuseredditlookatme
@@stefanoolivotto2391 Same. I came here thinking I'll learn something since I am terrible at math. What I saw here was what I would recommend people in classes 6-8 not to do. If a 9th grader did this, I would be plain pissed.
@@sistemsylar r/ihateredditlookatme
Ngl, the fact that a major part of the video told about the problems I was bad in when I was bad in maths in general, and as I practiced like hell and became good at maths, these were the mistakes that were weeded out, I can confirm these are the mistakes that mess you up the most
Thank you! This is very helpful for me as a college student because my knowledge about math from elem to high school has become vague.
I make some of these mistakes. I dropped out of high school when I was 17 and didn't go farther then algebra, got my GED when I was 26 and started college for Engineering when I was 31. Theres nothing wrong with making the mistakes. However, there is something wrong if your not noticing your making these mistakes and continue to do so. I'm now in cal 2 and proud of how far I've come.
good on you
Good for you. Keep going. My mom finished her RN degree in her 40s. She was the head boss of 2 nursing homes in my parish (Louisiana).
3:08
In german we say "Aus Summen kürzen nur die dummen." -> Only the silly ones reduce out of sums
And because in german it rhymes the students (mostly) remember it ✌️
Kürzen in Summen tun nur die Dummen meinte unser Klassenlehrer immer lol
I'm two years late but I love this
Thanks a million! This video will surely help me in the future!
1:35 - Calc 3 student here, this one always confused me! I actually got a test question wrong in high school because my (unironically really smart and good Calc BC teacher) gave something like sqrt(x^2 + 25) and expected us to simplify it to x + 5. Then when I didn't do that, the problem got super messy and I got it wrong. After that, I always thought that you were allowed to do that and it's just rarely used. Now I know he was wrong lol
I think this happens a lot because we are taught such important math lesson so young. This is mostly pre algebra and algebra one which is taken around 13 years of age. Many people just do not have the maturity to take their education seriously at that point and wind up without the basic foundation. Having re-learned most of these concepts by self teaching from textbooks, all of these concepts are natural reflexes as I had the maturity to internalize the lessons.
Gonna show this to my students :)
I'm top of my year in maths (British year 10) and even I got caught out with some of these without looking hard enough, thanks!
The way you explained the first mistake, has me wondering whether you don't learn binomial formulas in the US.
In Germany, I learned the following 3 formulas for that (The first two are kind of the same if you consider negative numbers.):
(a+b)^2 = a^2 + 2ab + b^2
(a-b)^2 = a^2 - 2ab + b^2
(a+b)(a-b) = a^2 - b^2
They are drilled into the heads of students here the same way the Pythagorean Theorem is, with a lot of repetition.
Same in India
We don't explicitly teach that. We teach the rules of how to expand those expressions and point out those 3 as patterns that you can quickly recognize if you want to help save some time doing a calculation.
After tutoring for the past few years, mostly college level. I want to add a few more of my own geared towards upper level math. The mistakes you mentioned still apply to a fair number of my students, even some math and physics majors, on occasion.
1. Not saying ± after taking the square root
2. Exponent and Logarithm rules (something about simplification of these really trips up some students)
3. Basic trig identities (mainly geared at calc students who forget unit circle and pythagorean identity)
4. Forgetting to take the derivative of the inside function when doing chain rule
5. Forgetting to write dx for implicit differentiation
6. Forgetting to write differentials when writing integrals
7. Forgetting + C when calculating indefinite integrals
8. Forgetting to substitute the original function back in after a u-sub or trig sub.
9. Mixing up partial and complete derivatives
10. Using a ' to notate a derivative in a multivariable function
11. Forgetting the Jacobian
12. Taylor series
13. Mixing up trig functions and hyperbolic trig functions
14. Vector and matrix notation
15. Surface Integrals and Divergence Theorem
16. Laplace and Fourier Transforms (not understanding how to use a table)
17. Not normalizing orthogonal bases. (Especially physics students taking QM. A lot of nice properties come from orthonormal bases. If the wave function is not normalized, you can't use these properties)
18. My biggest pet peeve, between steps in a solution, stating all steps are equal. For example,
1+7x=15= 7x=14
=x=2
Not all of these are the student's fault. Some if thesr concepts are taught poorly. These common mistakes also depend on the level of math and physics a student is at. I don't expect a trig student to know derivatives obviously. When I am explaining a physics priblem to students who are done with Diff EQ but forgot how to use Taylor Series or how to properly write differentials, it can be difficult. I have been guilty of some of these in the past and I still sometimes make some of these mistakes.
omg i do 18
ill stop lol
but srsly half of those mistakes dont make sense to me, i mean i havent learned anything of the logarithms and differential stuff but it... sounds cool ig
For all the Einsteins down here...if you are already subscribed to major prep its because Science/Maths videos are in your interest thus this will obviously be basic, but I can assure you other hypothetical millions who could get a video like this in their recommended find this very useful.
Heard of the pareto principle. His fanbase also works something like that
Tangent of circle. In America they teach most of it by grade 5. Foiling, algebra and quadratics come at grade 6-8. Any high school level student in America that doesn’t know everything in this video isn’t prepared for high school. To be fair I don’t think it’s the fault of the student. Mathematics is taught pitifully bad in America.
“12/?=6” so many of these mistakes could be erased if we could tell/remind each other what the underlying question is! I’m still using many of these tips to both solve and tutor my fellow students
So useful to always keep in mind! Also really helpful to learn all this math verbiage in english! Thanks Zach
Well this was a lot more specific than I thought it was going to be haha. Not very applicable to engineering, physics or math students but I’d say it’s very common everywhere else.
Great video that I think could help a lot of people struggling with math
All those concepts are known to me, but I am happy to have seen this video and I have it to my favourites to see it again. I am watching regularly advanced math tutorial, but sometimes it is necessary to return to the very basics to not lose the focus from the basic logic.
I'm in the french equivalent of HIgh School (I think (equivalent to year 13 for british)) and if someone were to do any of those mistakes you pointed out he would be the worst at math in the entire school. I really hope that americans have better students because I don't know a single french in my family or school that would do these mistakes and US always claims that they are better than any other country where it seems to me that they are really bad at math.
I enjoy your video, keep up the good work it is really entertaining.
Have a nice day.
I was definitely guilty of a lot of these mistakes when I was in high school 😅 something like this could have saved me a lot of frustration
8:15 Remember, though, that’s only using the regular division key. If you use the fraction key, it will be separated into numerator and denominator. It can be confusing though in linear calculators, so I’d recommend only doing it in calculators which have a “natural” display (CASIO calls it “Natural VPAM”), which are probably most of them (including all graphing calculators I know of).
That's not true of all calculators, though. Most calculators do not have a separate fraction key.
Give me RPN any day.
I think this will help my students a lot. Thanks for making this video!
really enjoyed the video. thanks a lot. waiting for part 2
His tone shows frustration from his student's mistakes
Please make a Part 2, or another video for common errors in higher-level mathematics! I used to be in a rut with algebra, until I realised I was too focused on the notation/rules, rather than understanding and getting an intuition of the processes underpinning them. Great video!
Thank you!! Great video, i have definitely made many of these mistakes in calculus and physics.
I hope there is a part 2 to this!
This really helped me alot on my silly mistakes in calc class. Thanks!
I'm now teaching students who struggle in math, and fractions are the most frustrating, in fact my master thesis is on it. I'm actually learning things about fractions that I never knew, like why we flip the second fraction in dividing. So am always happy to see any of your videos, what may sound the simplest is sometimes the key to everything
WHY? why do we flip the frac while /?
If u haven't ever lost marks due to these mistakes, you aren't a student
No, if u haven't done such mistakes, you just a normal student. I don't know, how anyone can forgot these things from MIDDLE SCHOOL...
@Bitch u wanna say that American schools sucks?
Corey you would of made those mistakes in MIDDLE SCHOOL.
@@kdraws3361 Well, your spelling and grammar sucks. Maybe you don't either.
I had measles when I was in elementary school and missed 6 weeks of class as a result. I often wonder if during that 6 weeks I missed some arithmetic fundamentals. Back then we didn't have calculators or computers, much less videos like this one. I continue to feel like I'm playing catch up with basics. Thanks for this one.
This guys a lifesaver, thank you!
I loved math my whole life, and did very well in it, and I can tell you the most points I lost was from not slowing down and looking at what I was doing. So even a math major can get a lot out of this
Are you retired? If so what was your job?
1:47 "You can't really simplify any if these at all"
Complex numbers: "That's where you're wrong kiddo"
And then what
Well, you could just factor out the x^2 and then work out the rest...
just take my sub, cause you helped me in the things which were the most confusing and no one told me about them , I also asked my teachers but they only gave more confusion....thanks bro..thanks...❤
That 12/x =6 explanation just blew my mind