I don't think you realize how life changing this was, literally covered almost every misunderstandings of algebra that I ever had. Seriously dude, thank you.
I'm still not at cos or sin level in school, but the rest made me literally emote with embarassment. Like how the hell can a person even make such silly mistakes?!!
I did some of these mistakes in my first year A-LEVEL mathmatics, I really had to do alot of practice to get rid of them, Thank God in my final highschool year I was so proficient and never did such mistakes. You really need alot of practice to master algebra.
I love the sound editing on this its so funny, also the way you were correcting and teaching was also clear and concise. The editing kept me entertain while watching
Finishing up my math classes for my engineering degree- I was curious if I’d see any mistakes im not aware of but I’m comfy with all these and have definitely made pretty much all of these mistakes at one point. Makes me feel like I’ve learned it properly though!
@@xelp435 nah you shouldn't. I am a mechanical engineering major and I'm not that good at math but still managed to get A's in all the calcs and differential equations courses. You're good. Even the physics and engineering math is not that hard tbh.
@@Ascee1In India grade 9-10 is called high school and grade 11-12 is called higher secondary. But the saddest part of our curriculum is that our education system sucks and we have cut throat competition with a lot of pressure 😢
• Reference: 15:30 Here, with Error #2, I'd like to add a point: Mostly, when students see the square root function, they instinctively think of 2 solutions, +ve and -ve. But that isn't the case in some places. • Example Imagine the question √9 = ? Most students answer ±3, which is wrong. The answer is only +3. The square root function by itself denotes the absolute value only. But, there's a catch! Suppose the question is - If x² = 9, find x. Then x can assume 2 values +3, -3. The thing is, when we're just asked what the square root of a number is, then the answer is only the absolute value. However, when asked the square of what number can assume a given value, then the answer will be both ghe positive and the negative values of the square root.
yeahh i was confused by this exact thing for a long time(im going to sophomore year of high school ig) and the one thing that my teacher told me a few years back is to *factorize* and solve. so i would approach this question by subtracting the 9 from both sides and then solving the quadratic equation, x^2 - 9 = 0, which equates to x = +/- 3 ps. im currently a math olympiad student
Correct, because when x²=9, we write x=±√9. And then what's asked in question is the value of +√9. Hence we write 3. Had it been -√9, we would write -3
yeah and I'd like to add onto that what my teacher taught us: *√x²=|x|* so if the que is x²=9 we take root on both sides: √x²=√9 => |x|=3 and hence x=±3 that is if you know how modulus works
right, math should have been taught in a way thats manageable for everyone. For many people, they learned to hate math cuz of the way it was taught and so forth. Some kids can handle it but surely not everyone. I hated it until junior high then i actually started to be ok and was actually getting better in some ways. I was improving more in high school ironically. But i think it was that i didnt pay a whole lot of attention in elementary math back then. but honestly they should focus on the students needs more than just test scores. thats prob a reason why theres such a shortage in math teachers and math degrees. Math is a difficult subject if not handled properly. And honestly same goes for science for many people.
10:30 i used another method to get this answer: 3/x = 6, that means that x/3 = 1/6, multiplying both sides by 3 we get the answer of x = 3/6 which can be shortened further to x = 1/2
This is a good way to solve the problem. I would actually have done the exact same thing, but with a couple of extra steps: 3/x = 6 -> x*3/x = x*6 = 3 -> x*6/6 = 3/6 -> x = 1/2
I speak Spanish and a little English and I must say the truth that I understand mathematics more in another language than in my language, I don't know if this happens to anyone else, but I love the idea of learning and at the same time improving my way of understanding English in mathematics.
It happens to me! Probably because I watched math tutorials on RUclips that are in English, when it comes to math tutorials in my native language, I don't understand anything, hahaha 😭
If you think about it, "I don't make 90% of these mistakes" could mean you make 100% of those mistakes (or any other percent figure, just not 90). A more precise way of expressing your intended meaning would be "I avoid 90% of those mistakes."
Yeah bro I am from India and we learn this level of maths in 5th grade in high school we learn advanced calculus, vector 3d geometry co-ordinate geometry like hyperbola ellipse and all.
@@dilchorff Yeah, absolutely. As I wrote in the original comment, these minor errors were not common in my life. It would be wrong to say I never made those mistakes, but I made mistakes for a short period of time after first learning a new concept. Then, after a while, I would never look back with those mistakes.
The way I explain Number 2 to students is that you can ONLY cancel terms that are multiplied to the entire numerator and entire denominator. In the numerator of your example, the 2 is only multiplied to the x, not the rest of the numerator, so you can't cancel it with anything in the denominator
*1.True, because we square the 4. The minus sign is not in brackets with the 4. *2. False, because this is (x + y + z)(x + y + z) *3. False, because here we have to first factorise 4, then use the exponent rule. So you finally get 2 to the power x + 2 *4. True, because we square everything in the brackets. *5. False. The Y's are not factors, they do not cancel out. They could only be cancelled if the y in the numerator had been multiplied, but it's not. *6. False. We need a common denominator in order to add fractions. *7. True, because it's (-2)(-2)(-2) *8. False, because Cos is a function not a pronumeral. (I'm a mum revising my high school maths, please tell me if I'm wrong - but also be kind!)
THIS is truly valuable info!!!!! We need a big ‘ol problem worksheet (with solutions) to accompany the video, and I would pay money for that!!! Many thanks for this enjoyable and informative lesson!
Number seven. The moment that you said when that answer of two appeared, plug it back in to the original equation to check your work. Absolutely beautiful. I tutor in a high school, but sub mostly at the sophomore level. One of my obsessions is to teach them the skill of “check your work“. It is remarkable to me how many students don’t understand what that even means. So many have asked me, “what does that even mean, do I just do the problem a second time?“ when school starts in September, and I am in front of the class for the first time, I plan to go through your top 10 list. Probably for the whole block. Hopefully it will avoid the look of horror on my face a few months in.
I'm a math tutor in a community college, this is very spot on. Especially forgetting to divide all terms by the numerator, and literally anything with a fraction 😭
that's why you need to understand math, as a highschool senior, these mistakes i haven't seen since middle school because, these are math fundamentals, but i'm glad a lot of student cleared their misunderstandings
I'm in grade 12 studying for my advanced final exam in maths constantly achieving about 90%. I needed no help, but I watched the video anyway, in order to understand the mistakes made by others, so I can help them.
Isn't it better to simply move one term to the other side of thr equal sign? Eg: 3/x = 6 Move the x to the 6, => 3 =6x Then move the 6 to the 3 => 3/6 = x => x = 1/2
We need to change the way negatives and other operations are taught. Perhaps if negatives arent taught until multiplication is taught so that students can internalize that there is an implied operation when you have something like -2? That way you can teach it as (-)(2) = -2 So with exponents (-)(2)^3 = -2^3
btw for √x, it is not always ±x. it depends on the context of the QUESTION itself. if they are asking for the length of the side of a square that has an area of 9cm², the answer is not ±3cm but only +3cm as length is not measured as a negative quantity. hope this helps, since proper application of common sense in questions is something that is very rare in students.
8:25 I think this method is also useful. Although it might have its downsides. The method is: (a/b) + (c/d) = ( bc + ad / bd) The brackets here are just meant to make it easier to read.
Yoo im an indian and gotta say thks very much for this vid man helped me a lot Oh and i saw some indians and asians in the comments saying that they never made these kinda mistakes and i apologise on behalf of them they're prolly just tryna show off or sumin im really sorry their behaviour
Everyone has made these mistakes. Every single one. They are just liars. I'm saying this as an Indian. The people who comment that are such lowlifes wishing for attention 🫢
To all Indian in comment section first if are watching this vedio by searching it you are 👑 but is you find it accidentally and feeling proud about not making mistakes like this just remember learning mistakes and studying failure gives us a big lesson as compaired to success and being infallible
In the 5th mistake the equation is 3/x=6. Here; The 3 is in division with x so if you drang it to the other side, it goes into multiplication with 6 which is 18 And you could check by 3/18=6
Thanks sir. Well there is an identity where many students get confused i.e a²-b²=(a+b)(a-b) so here the problem, for example if I ask what is (x⁸-1)(x⁸+1) then some some some students say that it should be (x⁶⁴-1) but its wrong it should be (x¹⁶-1). Now please don't comment that I'm from Asia and we learn this in nursery 🤠..
11:49 Just a question: I remember the usual sinoid formula, and it stated that in the part of (x-c) indicates the shifting of the graph to left or right. So, how is this possible when the c=y? ‘y’ is definitely a variable in a sinoid formula, so how should I interpret this? Edit: Or does the result just count as a number (a degree to be more specific)?
These are the most basic level rookie mistakes that only a kid can manage to do. Please make a video on how yo deduce information out of a question. (Like in higher level integration, binomial theorem etc problems
Ok. As someone who hasnt graduated but loves math and plans on teaching it. The first mistake is just kinda nitpicky. Even people who understand math properly see a -3 and think a negative number, not a positive three multiplied by negative one. So while yes it is technically the wrong answer to say -3^2 = 9. Most people are going to look at that -3, even your mathematicians, and think -3, not -1(3), 99% of the time.
You can use (a + b)^2 = a^2 + 2ab + b^2 identity. The video is trying to suggest writing (a + b) * (a + b) to avoid making an error. Sounds like you do not need that extra step.
There will always be students who make silly mistakes, even if they know better (maybe because of lapse of focus), but if it's a recurring theme and for a significant number of students in a class then you've got a failing teacher.
Also, nobody's talking about this guy's attitude: "Here are the top ten mistakes that are costing you marks and frustrating your teacher." Jeepers, mister teacher, I'm so sorry I frustrated you, let me just unalive myself! Failing teachers blame; good teachers encourage.
Wish there was youtube videos like these 10-15 yr ago 👍 good work. Its great to have people who are passionate about subjects and shows why math is important in life. Than having people who only teach it to get paid.
It's the same thing PEMDAS-Parenthesis,exponents,multiplication,division,addition and subtraction BEDMAS-bracket(same as parenthesis),exponents,division,multiplication,addition and subtraction The order of division and multiplication don't matter as they are both treated equally and should be taken from left to right And the acronym like pemdas and bedmas varies from place to place
NOTE: ^ = exponent symbol. QUESTION #1: -4^2 = -16 -4^2 = -1(4)^2 = -1(4)(4) = -16 L.S. = R.S. Therefore, this statement is TRUE. _________________________________________________________________________________________________________________________________________ QUESTION #2: (x + y + z)^2 = x^2 + y^2 + z^2 Remember: apply the FOIL method for this question. (x + y + z) (x + y + z) = x^2xyxz + yxy^2yz + zxzyz^2 ≠ x^2 + y^2 + z^2 L.S. ≠ R.S. Therefore, this statement is FALSE. _________________________________________________________________________________________________________________________________________ QUESTION #3: 4(2^x) = 8^x You can’t multiply a base of a power (i.e., 2x) by a constant (i.e., 4). Therefore, this statement is FALSE. ________________________________________________________________________________________________________________________________________ QUESTION #4: (5x)^2 = 25x^2 (5x) (5x) = 25x^2 L.S. = R.S. Therefore, this statement is TRUE. ________________________________________________________________________________________________________________________________________ QUESTION #5: (x+y)/y = x Remember: divide both terms from the numerator (i.e., x and y) by the denominator (i.e., y). x/y + y/y Note: y/y cancel out each other. = x/y = x/y ≠ x
L.S. ≠ R.S. Therefore, this statement is FALSE. _________________________________________________________________________________________________________________________________________ QUESTION #6: 3/4 + 7/2 = 10/6 3/4 + 7/2 Remember: make sure that both the denominators have the same LCDs. The Lowest Common Denominator (L.C.D.) for 4 and 2 is 8. =6/8 + 28/8 =34/8 =17/4 OR 4 1/4 L.S. ≠ R.S. Therefore, this statement is FALSE. ________________________________________________________________________________________________________________________________________ QUESTION #7: (-2)^3 = -8 (-2)(-2)(-2) = -8 L.S. = R.S. Therefore, this statement is TRUE. ________________________________________________________________________________________________________________________________________ QUESTION #8: COS(x - y) = COSx - COSy This statement is FALSE because you can’t treat a function (i.e., COS) like a number and distribute them into their own argument.
Your solution for Q6 is correct, but your terminology is not. The Lowest Common Denominator (LCD) of two fraction is the Least Common Multiple (LCM) of the two denominators, which is written as "LCM(x,y)= z". In this case it would be LCM(4, 2) = 4. Whenever one denominator divides evenly into the other it is always the LCM will always be the highest of the denominators. How to calculate the LCD in your head: If the two numbers has common factors then you first factor these common factors out, multiply the remainding factors and the multiply by the common factors: 4 = (2)*2, 2 = (2)*1. The common factor is (2). Divide both number by that common factor, i.e. 4/(2) = 2 and 2/(2) = 1. Multiply these remainding factors i.e. 2*1 = 2, and then multiply by the common factor, i.e. 2*(2) = 4. This LCD is the Lowest Common Denominator of the two fractions. You can see that you don't have the LCM of the two fraction, as you can reduce the fractions to 3/4 + 14/4, i.e. lower, but still common denominator. What you did was cross multiplication, i.e multiplying both top and bottom of one fraction by the denominator from the other fraction and v.v.
@@Escviitash eh well you are kind of not following laws of what is an lcm but at the end of the day it still simplifies so its okay if you take 8 as the lcm since at the end of the calculation, it still simplifies back to 17/4
On 7... it was 3(2to the power of x)=36 so i moved the 3 to be 2power x=12 but then the answer is log2(12)=x which my brain tells me is wrong cuz there is no way they would complicate x that much+i dont know what 3×(2 power log2(12)) is... but on the other hand again i need it to be 3(12) so i need the 2 to be 12 which isnt possible with normal numbers so log2(12) makes sense Edit: guess am correct but i was so ready to be wrong
As a sixth grader who loves Maths, I solved everything correctly except the sin and log one, I literally have no idea what they are... Edit: before anyone replies, yes, I'm Asian.
I was just like you, now i am in 9th grade. I'll explain log aka logarithms for you. So when you have a power, say 3 to the power of 2 which obviously equals nine, which we'll write down as 3²=9. When you solve for nine, aka 3²=x, to solve for x all we have to do is just evaluate therefore solve the power. When you solve for 3, the base of the power (powers are the base and the exponent in case you don't already know) you will just take the square root. So x²=9 which √x²=√9 therefore x=3. But when we solve for the exponent we use log, so 3^x=9 therefore x=log3(9). So logarithms essentially represent the exponent of a power, which if you understand will help you determine their properties. Essentially when we solved for 9, we knew the base of the power and the exponent and that is how our equation was written, when we solved for 3 we knew the exponent and the evaluation or arithmetical solution of the power and when we solved for the exponent 2 we knew the base of the power which is also the base of the logarithm (that's how it's called) and the solution. Here's the proper definition of a logarithm: A logarithm is the inverse function of its respective exponential equation.
It seems trigonometry hasn't been introduced to you yet, but you might encounter it in upcoming grades. Yes, trigonometry is indeed one of the most complex topics
I was you in 6th grade. Luckily, my math teacher taught me trig one on one because I was so curious to learn about new concepts. I'm in 9th grade now and doing some real crazy calculus stuff. I'm not asian though.
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I don't think you realize how life changing this was, literally covered almost every misunderstandings of algebra that I ever had. Seriously dude, thank you.
You guys call this algebra?
Habibi grab a 11th grade algebra textbook from India
He may be in 7th or 8th grade@@SelmoonBhai
@@SelmoonBhaiman nobody cares respectfully
@@SelmoonBhai or maybe 🤯 hear me out, hes here to fix his mistakes as a beginner 🤯🤯🤯
@@SelmoonBhaichill out bro
Not gonna lie. As a dude in the 12th grade. These are the mistakes someone who just memorizes math, instead of understanding it, would do.
Yep, definitely!
yeah you gotta put the extra effort into understanding it
Hii ,where are you from??@@aezurefx
But someone said "never understand maths"
The higher you go, the more bullshit it becomes
There’s two type of reactions while watching this
** 10^10 levels of pain as you watch the mistake**
“Oh, that’s how you do it”
I am one of them of the first category... I am also a teacher and when I see these I am also flabbergasted.
I'm not very good at math(and by that I mean compared to my asian peers) so I'm more of a "yea that's a reasonable mistake to make)
@@kkTeaz Same here 🥲
Im both these
I'm still not at cos or sin level in school, but the rest made me literally emote with embarassment. Like how the hell can a person even make such silly mistakes?!!
I did some of these mistakes in my first year A-LEVEL mathmatics, I really had to do alot of practice to get rid of them, Thank God in my final highschool year I was so proficient and never did such mistakes. You really need alot of practice to master algebra.
Doesn't the same apply to every skill?
I love the sound editing on this its so funny, also the way you were correcting and teaching was also clear and concise. The editing kept me entertain while watching
I agree
for the last tip you can remember that (a+b)^2 = a^2 + b^2 + 2ab, so you dont have to actually multiply it out every time
It's also an easy way to find the roots of polynomials since if you factor it back in the number added or subtracted will be a root.
Don't you learn that in the US?
Yes a plus b the whole square is equal to a square plus two ab plus b square is very simple
Ohh i remember that from 8th grade😂
For higher powers, you can draw a pascal's triangle and look at the shape. Ofcourse, this is not an efficient way, but simply just a way.
I had physical pain watching the students solve.
Yeah fr
Same
Same
I am 8th grade I could solve almost every thing
@@Ward_Zeidansame bro 😭
Finishing up my math classes for my engineering degree- I was curious if I’d see any mistakes im not aware of but I’m comfy with all these and have definitely made pretty much all of these mistakes at one point. Makes me feel like I’ve learned it properly though!
which type of engineering ?
I’m going into engineering but I am a bit discouraged of the math, should I be worried?
@@xelp435 nah you shouldn't. I am a mechanical engineering major and I'm not that good at math but still managed to get A's in all the calcs and differential equations courses. You're good. Even the physics and engineering math is not that hard tbh.
I am in Grade 9. This video cleared all my doubts. Thanks for the help.
Hopefully you are in matric now
@@fksa3330 Yeah Hopefully😅❤
But isn’t grade 9 still middle school ?
@@Ascee1Depends. In the US it's freshman year of high school, and in other countries it can be considered middle school.
@@Ascee1In India grade 9-10 is called high school and grade 11-12 is called higher secondary. But the saddest part of our curriculum is that our education system sucks and we have cut throat competition with a lot of pressure 😢
• Reference: 15:30
Here, with Error #2, I'd like to add a point:
Mostly, when students see the square root function, they instinctively think of 2 solutions, +ve and -ve. But that isn't the case in some places.
• Example
Imagine the question √9 = ?
Most students answer ±3, which is wrong. The answer is only +3.
The square root function by itself denotes the absolute value only.
But, there's a catch! Suppose the question is -
If x² = 9, find x.
Then x can assume 2 values +3, -3.
The thing is, when we're just asked what the square root of a number is, then the answer is only the absolute value.
However, when asked the square of what number can assume a given value, then the answer will be both ghe positive and the negative values of the square root.
Yeah cuz answer for a sq root cant be -ve
Good point!
yeahh i was confused by this exact thing for a long time(im going to sophomore year of high school ig) and the one thing that my teacher told me a few years back is to *factorize* and solve. so i would approach this question by subtracting the 9 from both sides and then solving the quadratic equation, x^2 - 9 = 0, which equates to x = +/- 3
ps. im currently a math olympiad student
Correct, because
when x²=9, we write x=±√9. And then what's asked in question is the value of +√9. Hence we write 3. Had it been -√9, we would write -3
yeah and I'd like to add onto that what my teacher taught us:
*√x²=|x|*
so if the que is x²=9 we take root on both sides: √x²=√9
=> |x|=3
and hence x=±3 that is if you know how modulus works
I swear math is the worst taught subject in the world. Most of us never properly learned or weren't even taught some of these basic principles.
right, math should have been taught in a way thats manageable for everyone. For many people, they learned to hate math cuz of the way it was taught and so forth. Some kids can handle it but surely not everyone. I hated it until junior high then i actually started to be ok and was actually getting better in some ways. I was improving more in high school ironically. But i think it was that i didnt pay a whole lot of attention in elementary math back then. but honestly they should focus on the students needs more than just test scores. thats prob a reason why theres such a shortage in math teachers and math degrees. Math is a difficult subject if not handled properly. And honestly same goes for science for many people.
Or just....learn it urself
Wrong...try history.
@@sam-xh2cy ppl nowadays don't really understand the significance of self study, they want to be spoonfeeded
@@bata3258what’s the point of going to school then🥹. Self study is efficient and fine too, but to self study basics when it should already be taught??
Hi!
I'm a Math teacher from Brazil and my students make same mistakes here! Unbelievable 😮
Hence proved, maths is universal 😅
Same in europe
Very Nice Presentation ❤
Not for JEE aspirant
@@nodistraction5857mf you from allen or what. Many do silly mistakes even i did in my recent exam
10:30 i used another method to get this answer:
3/x = 6, that means that x/3 = 1/6, multiplying both sides by 3 we get the answer of x = 3/6 which can be shortened further to x = 1/2
This is a good way to solve the problem. I would actually have done the exact same thing, but with a couple of extra steps:
3/x = 6
-> x*3/x = x*6 = 3
-> x*6/6 = 3/6
-> x = 1/2
I would have done cross multiplication but that works too
Wow congrats 🎉
Just do the cross multiplication bro 💀🥶
Same
I speak Spanish and a little English and I must say the truth that I understand mathematics more in another language than in my language, I don't know if this happens to anyone else, but I love the idea of learning and at the same time improving my way of understanding English in mathematics.
yeah same
It happens to me! Probably because I watched math tutorials on RUclips that are in English, when it comes to math tutorials in my native language, I don't understand anything, hahaha 😭
You said a little English but your english is good tho
Happens to me too, as the mathematical words used in English are easier to understand than the mathematical words used in Bengali.
I'm a math course student, and while we are a lot more advanced than this it helps to refresh the memory somewhat.
As an Indian and a weak student in maths I'm proud to say that I don't make 90% of these mistakes
😂😅
If you think about it, "I don't make 90% of these mistakes" could mean you make 100% of those mistakes (or any other percent figure, just not 90). A more precise way of expressing your intended meaning would be "I avoid 90% of those mistakes."
@@pythondrinkI agree
@@pythondrink he is an Indian English is not his first language so...
@@salmaelkassimi6646English is widely spoken throughout India, i doubt he’d have issues learning
Being an Asian I can't relate to this video. I never made these mistakes
You can tell this now, but are you sure, you could tell this 3 years ago!!!
Yeah bro I am from India and we learn this level of maths in 5th grade in high school we learn advanced calculus, vector 3d geometry co-ordinate geometry like hyperbola ellipse and all.
@@dilchorff Yeah, absolutely. As I wrote in the original comment, these minor errors were not common in my life. It would be wrong to say I never made those mistakes, but I made mistakes for a short period of time after first learning a new concept. Then, after a while, I would never look back with those mistakes.
@@sire_99 wait is that not normal in the west?
Bro then why did search for this video 😂
The way I explain Number 2 to students is that you can ONLY cancel terms that are multiplied to the entire numerator and entire denominator. In the numerator of your example, the 2 is only multiplied to the x, not the rest of the numerator, so you can't cancel it with anything in the denominator
Yup thanks for pointing this out, was a bit confused why he didn't cover it lol
As a middle schooler, our math teachers taught us how to stop making the mistakes, except mistake 4 because we haven't done functions yet
Yes its taught in 9 but the functions and everything rated to it is taught in 11 and 12
brooo!!!???
whatt!??
only watched till the first mistake and my mind is already expanding in all directions smt crazy good thanks brother
I am also a high school math teacher. Spot on!
*1.True, because we square the 4. The minus sign is not in brackets with the 4.
*2. False, because this is (x + y + z)(x + y + z)
*3. False, because here we have to first factorise 4, then use the exponent rule. So you finally get 2 to the power x + 2
*4. True, because we square everything in the brackets.
*5. False. The Y's are not factors, they do not cancel out. They could only be cancelled if the y in the numerator had been multiplied, but it's not.
*6. False. We need a common denominator in order to add fractions.
*7. True, because it's (-2)(-2)(-2)
*8. False, because Cos is a function not a pronumeral.
(I'm a mum revising my high school maths, please tell me if I'm wrong - but also be kind!)
That's correct
*2: False, cuz (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx
no it's not wrong bcuz if you multiply what he said you will the formula you wrote
3.False , but it can be true if x= 1😊
Hi a Mum,I'm zdtf
As a math student, i nearly had a heartattack watching the last mistake.
THAT'S JUST (a+b)² = a²+2ab+b² !!
THIS is truly valuable info!!!!! We need a big ‘ol problem worksheet (with solutions) to accompany the video, and I would pay money for that!!!
Many thanks for this enjoyable and informative lesson!
Number seven. The moment that you said when that answer of two appeared, plug it back in to the original equation to check your work. Absolutely beautiful. I tutor in a high school, but sub mostly at the sophomore level. One of my obsessions is to teach them the skill of “check your work“. It is remarkable to me how many students don’t understand what that even means. So many have asked me, “what does that even mean, do I just do the problem a second time?“ when school starts in September, and I am in front of the class for the first time, I plan to go through your top 10 list. Probably for the whole block. Hopefully it will avoid the look of horror on my face a few months in.
I'm a math tutor in a community college, this is very spot on. Especially forgetting to divide all terms by the numerator, and literally anything with a fraction 😭
What are you doing here probably learning 😅
College students? 💀
No way collage students do that.
@@arnoygayen1984 students who make collages might
Thanks sir. Because of this video I have cleared many doubts regarding subtraction,multiplication, fraction and exponent
that's why you need to understand math, as a highschool senior, these mistakes i haven't seen since middle school because, these are math fundamentals, but i'm glad a lot of student cleared their misunderstandings
I'm in seventh grade.
And for the sixth one…… Damn bro how do students even think like that
Huh
I have the same question man... did they think it was 3/3 or something?
I'm in grade 12 studying for my advanced final exam in maths constantly achieving about 90%.
I needed no help, but I watched the video anyway, in order to understand the mistakes made by others, so I can help them.
who
@@Zkflamesasked
Anyways it's PEMDAS not BEDMAS.
@@bebektoxic2136 it doesn't matter really because they're the same thing
It's different in other countries@@bebektoxic2136
Americans: Oh! I can relate with these.
Asian: It was 18 min of pure pain.
Isn't it better to simply move one term to the other side of thr equal sign?
Eg: 3/x = 6
Move the x to the 6,
=> 3 =6x
Then move the 6 to the 3
=> 3/6 = x
=> x = 1/2
thats exactly what iam thinking
As an inspiring math teacher, I approve this video. Great job explaining!
We need to change the way negatives and other operations are taught. Perhaps if negatives arent taught until multiplication is taught so that students can internalize that there is an implied operation when you have something like -2? That way you can teach it as (-)(2) = -2
So with exponents (-)(2)^3 = -2^3
1. True
2. Its x² + y² + z² +2(xy + yz + zx)
3. 4 × 2^x
4. True
5. 1 + (x/y)
6. 17/4
7. Right
8. Cos(x-y) = cos x cos y + sin x sin y
thank you bro
For the third one you can do 2^(x+2), but I would also rather use 4 x 2^x instead
5th will be x+y/y=x
x+y=xy..?
Dude for number 1, - 4 × - 4 = + 16, remember - × - = +
8th is incorrect,the correct answer is sinexcosy - cosxsiney
btw for √x, it is not always ±x. it depends on the context of the QUESTION itself. if they are asking for the length of the side of a square that has an area of 9cm², the answer is not ±3cm but only +3cm as length is not measured as a negative quantity. hope this helps, since proper application of common sense in questions is something that is very rare in students.
Great video! And agreed - binomials and trinomials are trouble!
10:10
We can solve this by cross multiplication
It's right or not
18:00
We can solve with the identity
(a+b)² = a² + b² + 2×a×b
Yes or no
In the last one you can do:
(x+3)²
X²+2*x*3+3²
X²+6x+9
（a square ➕2ab➕b square）this is an identity
8:25
I think this method is also useful. Although it might have its downsides. The method is:
(a/b) + (c/d) = ( bc + ad / bd)
The brackets here are just meant to make it easier to read.
I got panic attack by watching this. Respect to all math teachers who deal with these mistakes!!!
7:11 I feel this is the dumbest mistake one can make even though I am bad at math😢😅
Yoo im an indian and gotta say thks very much for this vid man helped me a lot
Oh and i saw some indians and asians in the comments saying that they never made these kinda mistakes and i apologise on behalf of them they're prolly just tryna show off or sumin im really sorry their behaviour
Exactly lol
Everyone has made these mistakes. Every single one. They are just liars. I'm saying this as an Indian. The people who comment that are such lowlifes wishing for attention 🫢
16:59 wtf? We have a pure equation for this type of questions 💀
(a²+2ab+b²)
To all Indian in comment section first if are watching this vedio by searching it you are 👑 but is you find it accidentally and feeling proud about not making mistakes like this just remember learning mistakes and studying failure gives us a big lesson as compaired to success and being infallible
7:03 the way I calculated it was by simplifying it, 1/5=0,2 and 1/2=0,5 and ()=*x so 3*0,2+0,5 and 3*0,2=6 and +0,5=1,1
Why am I here? Im a junior mechanical engineering major.
😂, because you are Engineer
Congratulations 🎉
😀
Good for you no one cares
Same lol. I was just studying ordinary differential equations
Wish I could find this video sooner had to find all of them hard way
Hi! I'm from India and these are the most common mistakes we make
True😂
I thought you guys were the smart ones
@@ari-man we do make these mistakes tho, in 2nd grade
ah here we go again. pajeetbros with their "saar! we learn dis shite in de PRESCHOOL! BUT we don't learn how to use a toilet though... Sorry sirs!"
@@Shubh_42 Sahi kaha 😂
In the 5th mistake the equation is 3/x=6.
Here;
The 3 is in division with x so if you drang it to the other side, it goes into multiplication with 6 which is 18
And you could check by
3/18=6
3/18 is not 6 it is 1/6
0:09 "... and frustrating your teacher". Well, a Math mistake doesn't even come close to being bad as a Pedagogical mistake like that.
17:30 you can also apply (a+b)^2, makes it easier
As a highschool student I have never done them wrong and this is my achievement. Also got got the highest marks in exam
Great
Thanks sir.
Well there is an identity where many students get confused i.e a²-b²=(a+b)(a-b) so here the problem, for example if I ask what is (x⁸-1)(x⁸+1) then some some some students say that it should be (x⁶⁴-1) but its wrong it should be (x¹⁶-1). Now please don't comment that I'm from Asia and we learn this in nursery 🤠..
In Germany we say "Aus Summen kürzen nur die dummen!"
Honestly thank you soo much for making this vid! Super helpful
Thankyou ,this video was so helpful for me. 😊
11:49
Just a question: I remember the usual sinoid formula, and it stated that in the part of (x-c) indicates the shifting of the graph to left or right. So, how is this possible when the c=y? ‘y’ is definitely a variable in a sinoid formula, so how should I interpret this?
Edit: Or does the result just count as a number (a degree to be more specific)?
I'd answer your question if you specify a bit more, and say what situation you're referring to from ground up
This video taught me more than my math tutor ever did
In -2x=8 you can also simply multiply the equation by -1, then you have 2x=-8 and that equals -4 too
hmm. thats right
So helpful as a sophomore❤ Thank you professor😅
These are the most basic level rookie mistakes that only a kid can manage to do. Please make a video on how yo deduce information out of a question. (Like in higher level integration, binomial theorem etc problems
That's literally the point of this video
Ok. As someone who hasnt graduated but loves math and plans on teaching it. The first mistake is just kinda nitpicky. Even people who understand math properly see a -3 and think a negative number, not a positive three multiplied by negative one. So while yes it is technically the wrong answer to say -3^2 = 9. Most people are going to look at that -3, even your mathematicians, and think -3, not -1(3), 99% of the time.
17:11 why instead can't we just use the a+b the whole squared identity
You can use (a + b)^2 = a^2 + 2ab + b^2 identity. The video is trying to suggest writing (a + b) * (a + b) to avoid making an error. Sounds like you do not need that extra step.
There will always be students who make silly mistakes, even if they know better (maybe because of lapse of focus), but if it's a recurring theme and for a significant number of students in a class then you've got a failing teacher.
Also, nobody's talking about this guy's attitude: "Here are the top ten mistakes that are costing you marks and frustrating your teacher." Jeepers, mister teacher, I'm so sorry I frustrated you, let me just unalive myself! Failing teachers blame; good teachers encourage.
12:37 i dont get it.. it should be log(x)×log(y)
Yeah
Wish there was youtube videos like these 10-15 yr ago 👍 good work. Its great to have people who are passionate about subjects and shows why math is important in life. Than having people who only teach it to get paid.
Maths hasn't exactly been my strongest suit but never in my life have i made these mistakes😭😭
Your math teacher when he/she sees it umm actually... Chal ghuthi 🤓
At 5:07 i was confused, isn't it PEMDAS and not BEDMAS? I never heard of BEDMAS before.
It's called different things
PEMDAS
BEDMAS
BODMAS
but the surmise is the same
It's the same thing
PEMDAS-Parenthesis,exponents,multiplication,division,addition and subtraction
BEDMAS-bracket(same as parenthesis),exponents,division,multiplication,addition and subtraction
The order of division and multiplication don't matter as they are both treated equally and should be taken from left to right
And the acronym like pemdas and bedmas varies from place to place
In Germany we say "Punkt vor Strich". (Dots before Lines) (• : before + -)
I think the last one we can simply say that it's open by (a+b)^2 formula which is (a+b)^2=a^2+2ab+b^2
NOTE: ^ = exponent symbol.
QUESTION #1: -4^2 = -16
-4^2 = -1(4)^2
= -1(4)(4)
= -16
L.S. = R.S.
Therefore, this statement is TRUE.
_________________________________________________________________________________________________________________________________________
QUESTION #2: (x + y + z)^2 = x^2 + y^2 + z^2
Remember: apply the FOIL method for this question.
(x + y + z) (x + y + z) = x^2xyxz + yxy^2yz + zxzyz^2 ≠ x^2 + y^2 + z^2
L.S. ≠ R.S.
Therefore, this statement is FALSE.
_________________________________________________________________________________________________________________________________________
QUESTION #3: 4(2^x) = 8^x
You can’t multiply a base of a power (i.e., 2x) by a constant (i.e., 4). Therefore, this statement is FALSE.
________________________________________________________________________________________________________________________________________
QUESTION #4: (5x)^2 = 25x^2
(5x) (5x) = 25x^2
L.S. = R.S.
Therefore, this statement is TRUE.
________________________________________________________________________________________________________________________________________
QUESTION #5: (x+y)/y = x
Remember: divide both terms from the numerator (i.e., x and y) by the denominator (i.e., y).
x/y + y/y
Note: y/y cancel out each other.
= x/y
= x/y ≠ x
L.S. ≠ R.S.
Therefore, this statement is FALSE.
_________________________________________________________________________________________________________________________________________
QUESTION #6: 3/4 + 7/2 = 10/6
3/4 + 7/2
Remember: make sure that both the denominators have the same LCDs.
The Lowest Common Denominator (L.C.D.) for 4 and 2 is 8.
=6/8 + 28/8
=34/8
=17/4 OR 4 1/4
L.S. ≠ R.S.
Therefore, this statement is FALSE.
________________________________________________________________________________________________________________________________________
QUESTION #7: (-2)^3 = -8
(-2)(-2)(-2) = -8
L.S. = R.S.
Therefore, this statement is TRUE.
________________________________________________________________________________________________________________________________________
QUESTION #8: COS(x - y) = COSx - COSy
This statement is FALSE because you can’t treat a function (i.e., COS) like a number and distribute them into their own argument.
Your solution for Q6 is correct, but your terminology is not.
The Lowest Common Denominator (LCD) of two fraction is the Least Common Multiple (LCM) of the two denominators, which is written as "LCM(x,y)= z".
In this case it would be LCM(4, 2) = 4. Whenever one denominator divides evenly into the other it is always the LCM will always be the highest of the denominators.
How to calculate the LCD in your head:
If the two numbers has common factors then you first factor these common factors out, multiply the remainding factors and the multiply by the common factors:
4 = (2)*2, 2 = (2)*1.
The common factor is (2).
Divide both number by that common factor, i.e. 4/(2) = 2 and 2/(2) = 1.
Multiply these remainding factors i.e. 2*1 = 2, and then multiply by the common factor, i.e. 2*(2) = 4.
This LCD is the Lowest Common Denominator of the two fractions.
You can see that you don't have the LCM of the two fraction, as you can reduce the fractions to 3/4 + 14/4, i.e. lower, but still common denominator.
What you did was cross multiplication, i.e multiplying both top and bottom of one fraction by the denominator from the other fraction and v.v.
@@Escviitash eh well you are kind of not following laws of what is an lcm but at the end of the day it still simplifies so its okay if you take 8 as the lcm since at the end of the calculation, it still simplifies back to 17/4
@@RGGBMGOno, he's right
That one educated unemployed friend on a Tuesday
Q5. x/y + 1 ≠ x
I'm in seventh grade taking AL 1 Honors, this video is very helpful
Question, shouldn't it be intuitive that 3 times ONE fifth is THREE fifths?
Oooo my comment got hearted, yay!
Don’t underestimate the stressing on an exam lmao
On 7... it was 3(2to the power of x)=36 so i moved the 3 to be 2power x=12 but then the answer is log2(12)=x which my brain tells me is wrong cuz there is no way they would complicate x that much+i dont know what 3×(2 power log2(12)) is... but on the other hand again i need it to be 3(12) so i need the 2 to be 12 which isnt possible with normal numbers so log2(12) makes sense
Edit: guess am correct but i was so ready to be wrong
In India we used to solve these kinds of problems in 4th or 5th grade 😂
18:17 Quiz
1. True
2. False
3. False
4. True
5. False
6. False
7. True
8. False
Indian 4th grade laughing in a corner
What is the name of the music/song at the end of the video, please?
1:50 ain't no way someone does that
you don't wanna know😂
17:28 and you can also try (a+b)²=a²+b²+2ab 😕
As a student
i really appreciate your work
also i need to confront my teacher about this
Lol, hope u didn't do anything stupid cause he actually failed question /mistake 6
15:55 x²=9
=> x² -9=(x-3)(x+3)=0
=> Solutions: x= ±3
This must be painful for you to see your students do lol
@@bryanc1604 you’re right! I guess I was ignorant when I commented that. Wish me luck next semester when I do take it :) All the best, Bryan.
lol this reply section.
Replies were deleted. What happened?
@Potato-so6zr ya
6:23 Problem 7 Solution
3(2^x)=36 => 2^x=12=2²·3 => x=2+log₂(3)
(Use fact that 2^x/2²=2^(x-2))
I swear if i lose marks about this 1:21
As someone who loves the quadratic formula, I actually never really thought of number 1, I am shocked. Thank you for telling me this.
Brooo the constant BWAAAAM is sending me 💀
Very awesome video though
These are actually life changing i used to get confused af at kumon but now i atleast understand more
this is gonna get students into universities
We need more stuff like this and u should make video on very basic mistakes that we mostly do.
3:33 why did his voice change?😂
Second student making a different mistake.
12:06, careful using the word "of" there. we do teach students that "of" means multiply. ;)
1:29 just use your calculator. Hehe
ppr 2 cannot
one is x/x+8 =1+x/8 .
Can remember one dude making this mistake back in 11th grade .
Rn he's is in BITS Pilani main campus.
0:32 i always made this mistake😭
Bro , am i the only one who misses those multiplication math worksheets we got in preschool, Math was fun back then 😢❤
1:42 Oh trust me nobody is even this dumb to exist to make this mistake 😂
I used to do it when I was in 8 th but I practiced hard and was top god in maths in-class
i did this mistake in 6th grade
i did this once at 12th grade bc i forgor
Fact. You forgot about (a+b)^3 = a^3 + 3ab + b^3😁
That's so wrong! , it's (a+b)³=a³+b³+3ab(a+b)
(a+b)³=a³+b³+3a²b+3ab²
I wanna be an algebra teacher someday and I think this being the first day of class is a GREAT idea
As a sixth grader who loves Maths, I solved everything correctly except the sin and log one, I literally have no idea what they are...
Edit: before anyone replies, yes, I'm Asian.
Ok
I was just like you, now i am in 9th grade. I'll explain log aka logarithms for you. So when you have a power, say 3 to the power of 2 which obviously equals nine, which we'll write down as 3²=9. When you solve for nine, aka 3²=x, to solve for x all we have to do is just evaluate therefore solve the power. When you solve for 3, the base of the power (powers are the base and the exponent in case you don't already know) you will just take the square root. So x²=9 which √x²=√9 therefore x=3. But when we solve for the exponent we use log, so 3^x=9 therefore x=log3(9). So logarithms essentially represent the exponent of a power, which if you understand will help you determine their properties. Essentially when we solved for 9, we knew the base of the power and the exponent and that is how our equation was written, when we solved for 3 we knew the exponent and the evaluation or arithmetical solution of the power and when we solved for the exponent 2 we knew the base of the power which is also the base of the logarithm (that's how it's called) and the solution.
Here's the proper definition of a logarithm:
A logarithm is the inverse function of its respective exponential equation.
It seems trigonometry hasn't been introduced to you yet, but you might encounter it in upcoming grades. Yes, trigonometry is indeed one of the most complex topics
I learnt trigo before log I'm currently in 11 th grade but there is no logarithm chapter neither it was in my lower grades
I was you in 6th grade. Luckily, my math teacher taught me trig one on one because I was so curious to learn about new concepts. I'm in 9th grade now and doing some real crazy calculus stuff. I'm not asian though.