10 Question True or False Math Test | Tricky Questions!
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- Опубліковано 27 чер 2024
- Welcome to JensenMath! In this video, I'm presenting you with a real brain teaser - a 10-question true or false math test that will truly put your mathematical knowledge to the test.
But beware! These questions aren't your typical run-of-the-mill problems. I've crafted them to tackle some of the most common misconceptions in math, spanning topics like square roots, trigonometry, logarithms, and quadratics. Even the most seasoned math whizzes might find themselves scratching their heads!
I challenge you to give these questions a try before watching the answers. Think you've got what it takes to ace this test? Don't worry if you don't - NONE OF MY STUDENTS HAVE EVERY GOTTEN A PERFECT SCORE!
Remember, if you believe the answer is false, be ready to back up your correction. Understanding the reasoning behind the solutions is just as important as getting them right.
And hey, if you're hungry for more math challenges or in need of extra help, head over to jensenmath.ca for FREE math resources that will sharpen your skills and deepen your understanding.
So, are you ready to put your math prowess to the ultimate test? Let's dive in and see if you can conquer these tricky true or false questions!
0:00 question 1
1:07 question 2
1:40 question 3
2:34 question 4
3:15 question 5
4:34 question 6
6:25 question 7
7:54 question 8
9:37 question 9
10:59 question 10
It's more precise to say that log(x²) equals 2log|x| and not just 2log(x)
Yes, surprised this wasn't pointed out given the previous questions!
i think its because log isnt defined for negative, so x has to be positive with or without the |.|
@@maxendre8165 Exactly
@@maxendre8165 ofc log is defined foor negatives
It's not more precise It's just the only true statement
Asymptote question tricked me.
Remaining, I got it right
I got that one on a different technicality- if you graph two functions together as with a system, one can touch the other’s asymptote.
You can also disqualify his question because no domain was specified, so you can just conveniently choose a domain for the function where intersecting the asymptote doesn’t ever happen, like (infinity minus epsilon, infinity).
All is fair with these kind of gotcha nonsense tests lol.
Same
Same
You got the last one right?
same
That's so evil of you!!! I got (6.5±0.5)/10
This is 5.0 or 7.0
@@zian010006 or 7, they mean they do not know whether to count question 10 as right or wrong.
√(-5) × √(-5) = -5
√5 × √5 = 5
why tf are you everywhere i go
@@w1nt_er why not
Nah bro i got x/10 where x is in superposition of 9 and 10
11:18 I choose to invoke the fifth and wish to speak to a lawyer
ah you got me on the last question
if the answer to that question is true, then 9 questions would be false and this one would be true but according to the question ALL 10 questions are false
if the answer to that question is false, then AT LEAST 1 question MUST be true but all 10 questions here would be false
Yup, it's paradox😢
I loved the 10 common math mistakes video but now I love this one even more! I only understood the first two at first and the 10nth question is a chicken and egg scenario where neither answer could work
A function can touch it's vertical asymptote. Consider the piecewise function f(x) = 1/x^2 if x≠0 and 0 if x=0. This function touches the vertical asymptote.
As someone with an amazing Hn Alg 2/trig teacher I got all 10 right. I the last one is a paradox so I chose no solutions 👍.
9/9 not counting the last one. Good video highlighting common errors and misconceptions I see with some of my students.
9/9, I'm not counting that last question.
The last one got me as it is aparadox. Nice video.
I'm not sure if it's a cultural thing (UK here), but when I was doing maths in school, we were always told that sqrt(25) is +/- 5, and you can only discount the negative if either the negative makes no sense (like finding a length), or it specifically says it (like +sqrt(25) ), more complicated questions involving square roots would use the positive due to the commutative properties of addition.
You can only get two values of the square root of you are dealing with algebraic problems. But if it’s only the square root of square root of the number then we have to take the principal square root
@@eclipseninja08 And thats just the most dumb manmade rule that exist in mathematics. Does the big rule book of mathematics say so? No, its just us humans not liking negative numbers
@@The_Commandblock
Maths is not about doing what makes you happy.
The whole point of this is to make the square root be a valid function. Otherwise it would fail the vertical line test. As to why this is important, Google it.
Also, this is necessary for any actual real world application of mathematics. Negative area or volume does not exist. The only reason a square root can represent two values when it comes to complex numbers is simply because there's no difference between i and -i
The whole point is to make square roots a one to one function. Nobody wants to deal with having extra useless negative solutions especially when they're useless for most geometrical applications.
@@flightyavian4580 After carefully considering your comment i came to the conclusion that you contradicted yourself.
1. Math is not about application, most mathematicians probably didnt know that their work would be very important in physics and engineering later on.
Thus, maths is also not based on our real world, but rather on complex ideas.
2. We all know that noone WANTS to deal with negative solutions (atleast a guy from the internet said that). However:
"Maths is not about doing what makes you happy"
3. The only reason why we are not respecting negative solutions is because ancient mathematicians didn't respect them
4. 1^½ = e^ln(1^½) = e^(½ln(1)) = e^(½*0) = 1
However 0 is not the only ln(1) another is for example 2πi so
e^(½ln(1)) = e^(½*2πi) = e^πi = -1
@@The_Commandblock
First of all, whoever invented square roots for whatever reason is mostly irrelevant now. Second of all, again I reiterate my point: negative solutions are redundant according to most of where this kind of maths is used. You have any kind of quadratic equation using scalars or talking about the number of stuff and so on, or anything involving area? Then a negative solution is stupid, because negative amounts of stuff doesn't exist. The square root may have represented both values originally, perhaps. But it doesn't now. That's the whole point.
Saying that the reason we don't respect them is because ancient mathematicians didn't either is completely false. Who told you that?
You really think math is some kind of conspiracy theory? No, this is just convenience. And I never contradicted myself. Already negative solutions are rejected a lot of the time when solving any sort of quadratic or so on system for area. Because they aren't actually true.
That isn't subjective; when you get a negative volume for something that can only be positive, that is often talking about a nonexistent unrelated shape that doesn't fit the bounds of what you were looking for. Square roots not representing the negative value is extremely useful in almost every application for it. Negative solutions are not.
Best I could do for last question:
FALSE. Because although this was a true or false test, it was required to correct the statement. So the correctio s we made qere also a part of the answer. not just 'false'
I answered "or"
Last one made me laugh 😂 9/10 corrext
The last one is "not True"
Or you could say:
log (3x²) = log (√3x)²
Therfore:
log (√3x)² = 2 log (√3x)
That is how I did it
the last one got me lol
Last question was counterintuitive
2:25 imagine a kid watch your video and do what you say in GCSE maths exam 😂
He would get full marks on that part...
For the last question: I can interpret it as saying that the answer that we got was false, not the actual answer is “false”, but the answer is always correct, therefore it cannot be false, meaning that “false” is the correct answer to the question
being a high school student I scored 8/10 ( you tricked me in Q5 and Q10 )
but it was fun :)
The answer to question 10 is the same as the answer to the question of "does the set that contains all sets the do not contain themselves contain itself?"
I was working in a field of characteristic 2 for question 1, so I got true, and the last question had the answer false. I get 10/10.
For question 5, perhaps I am misunderstanding, but if we have the piecewise function f(x)=1/x when x is positive, and f(x)=0 otherwise, then there will be a vertical asymptote at x=0, but f does touch the line x=0 at the point (0,0), meaning a function can touch its vertical asymptote.
doesn't work. The limit of f(x)=1/x for x approaching zero from the right is infinity. If at the same time f(x) equals zero, then f doesn't have a limit for x=0, and therefore there is no asymptote.
make more video on basic maths
Question 8 is neither true nor false as worded. It can be either. Without a quantifier, it's impossible to say. If the question was "For each x..." it would be false. If the question was "There exists x such that..." it would be true. With that I'm able to answer question 10: Definitely false.
Whit that the question 1 and 2 would also be hard to answer, because there is the Same thing. But in general you are right, that’s the reason why in Maths you have to define every variable you introduce. In the video it can be misleading, cause x is often used for something you search for.
That last question is basically when pinocchio says my nose will grow but 2.0
i got all 9 questions correct and to not let my score be undefined, i choose true for the last one, 9/10.
Sorry to let you know that it does not work 😂
5:00 we can actually do it quite faster rather than replacing the numbers.
b'=b/2=3
△'=(b'^2)-a.c=3^2-25.1=9-25=-16 the equation has no solution
The answer to question 10 is “or”
That third Question always triggers me, still got it right but Mathmaticians really destroyed math by not allowing all roots to be the solution.
I also absolutly hate that sqrt(x^2) when people treat it like an expression thats the same to the absolute value: abs(i) = 1; sqrt(i^2) = +-i
No they didn't. The whole point of this is to make the square root a valid function otherwise it would be utter nonsense. If you want the negative solution, use x to represent both.
@@flightyavian4580 That‘s so true. Also that sqrt(i^2)=+-i ist just dumb. The sqrt() isn‘t defined in complex Numbers for a good reason. Mathmaticians defined it in a way that all makes sense and it is easy to use it. It is just dumb to demand that the sqrt() has to have two values. That would make it very hard to use that Function in any way, because you always have to make differentiate the case where it is positiv und where it is negativ and when you want all Solution you can just Write a +- bevor that. It is just much easier to make Maths and to Analyse the real Numbers when you just say that it has one Solution. With that you can say that it is a number and you can make cool things With that and you know many things. With your Suggestion you can‘t do anything Chase sqrt(2) isn‘t a number anymore. And also With complex Numbers many people just don‘t understand what they mean and how to use them. You just take that i^2 is just -1 and use them just Like they are any other number. You Never ask yourself how they are realy defined cause just to say i^2=-1 isn‘t enough. They to Proof that a*i=i*a or any other rule and you find that you can‘t do it. You can‘t just take the sqrt(-1) or sqrt(i) and give it as an example, cause that is just undefined and sqrt(x^2)=|x| cause sqrt() is only defined in the positiv real Numbers. And you do it cause you want to derive more out of simple things like the Natural Numbers and Look what you can make there and extand it to more and more things Like Multiplication, there you find that you can use it in the Same way in the real Numbers, but there you also have to Prove it, what people did. But that doesn‘t work for the sqrt() as well, when you Go from the positiv rational Numbers to more complex Numbers. You can‘t just extaned this principle for more Numbers that well and so wie don‘t and make new things With what we can represent the same thing in anouther way in that it is well defined
Ok so If I mark the last one as true the answer becomes false, and if I mark it as false, the answer becomes true. So I guess It’s true and false at the same time 💀
Yep, this violates one of the proposition principles (No contradiction). So the answer finally is undefined.
Got baited to doing all this, and yeah got the maths all right.
9/9 The last question is self-referencing, so a paradox is created XD
The last question must a be a paradox, so niether, all in all 7 of 10 aint bad
Question no.10 aside, if ppl are getting any other questions wrong, they really need to go back to school. Ngl, i was really hoping it would be a decently hard test
8/10 as a new 9th grader, pretty happy with my result.
missed the second, then realized and got everything right
I missed question 7. I was not thinking about complex numbers. It would have been good to include a true question. Number 10 is just designed so that nobody can get 10/10, so I don’t think that counts.
I only got 1,6.7,8,10 questions right, since I'm a 9th grade student. I haven't studied sin yet. Also haven't read logarithm. But I had interest so I read but not too far i have basic knowledge abt it. Looks like I'm nice in algebra.
10 is the trickiest
x² + 6x + 9 = -16
(x+3)² + 4² = 0
(x + 3 + 4i)(x + 3 - 4i) = 0
So x = - 3 ±4i
First question: if a=b=c=0 the statement is true. So the question is not well defined. You have to ask, if the statement is always true.
Why did you settle on 'principle'? That's the noun. You want the adjective 'principal' = main.
Questions 5 and 10 tricked me, but I got all the other ones.
9/10
I Didn't get question 2 right because I didn't know that trig identity off the top of my head, and even though I knew it was false, we have to give a correction each time for the point, according to the rules.
And I got 10 right because I said False. False is correct here because the question is a paradox of course, so it is in a state of being neither true nor false. If I put false as my answer, points should be awarded, because only 9 out of 10 of the questions are false, and the last is neither. This doesn't cause a paradox because while The Real Answer is a paradox, but the correct answer need not be the only answer to which points are awarded, and since "false" is the closest to correct of the options we are given, and thus the most deserving of points, I will count it as point-worthy. And the correction of the statement is "the answers to the 10 questions on this test are not all false".
If you don't agree with my logic on allat, I don't blame you. I made it all up. BUT, he did also say we can grade ourselves, so I actually get 100/10. GG EZ
Only question wasn't sure of was 7. It wasn't factorable by real numbers, and wasn't sure if imaginary numbers counted. It wouldn't in algebra 1, but since imaginary numbers were given before and all questions so far was false I chose false. For the final one I chose undefined since all 9 previous were false, but you couldn't say true or false so I basically you can't answer.
the answer to 10 is true because there are no actual questions in the test, so the questions are made up and can have whatever answers they wish
For the 5 I just was thinking about constant, ti keep it simple
last one is a trick! thats a paradox
Compound Area please I don’t understand the really difficult ines
Question 3 is subjective. I would’ve got the answer wrong on a real test if I didn’t add plus or minus.
I got only 1st question right since I'm 9th grade student, i didn't studied sin, cos, tan etc. yet and I still get confused in √25 = ±5
8/9 of the question i got them right, just the asymptoth.
Who ever came up with the idea of the principle of a square root being only positive, should be banned from the historic records of great mathemations.
If you have x=9^0.5, it only has one solution because it’s a first degree equation. But x^2=9 has two solutions. I’d say if all you have is square root of nine, there are two solutions. It’s the x that makes the difference
8/9, last question unanswered, well played
11:17 paradox
I got all except the last one
8/10 because I didn’t know what an asymptote was
But you said that the unadorned root symbol returns the principal root.
10:12 it's 2log(x√3)
X^2 + 4 = 0
X^2 = (-4)
X = 2i or (-2i)
4:24 I got it right but I feel like it's not well formulated it looks like you say that an asymptote can never touch any function for exemple 2^x can never touch the x=5 function which is false
9/9. #10 is a paradox and therefore has no correct answer.
I see what you did there... Haha I got 9/10. Easy
7/10 (number 10 is impossible to get correct)
1: False, it should be a^2+b^2+c^2+2ab+2bc+2ac
2: False, sin(x+y)=sinxcosy+cosxsiny
3:False, sqrt(25)=5
4: False, the slope will be undefined
5: False, a function may cross an asymptotic in some cases.
6: False, A quadratic equation will always have solutions. That equation has no REAL solutions.
7:False, x^2+4=(x+2i)(x-2i)
8: False, sqrt(x^2)=|x|
9: False, the correct simplification is log(3)+2log(x)
10: If the answer is true, then the statement is false; but if the answer is false, then the statement is true. Therefore, 10 is a paradox.
* asymptote
basically this is a test where you have to resist the temptation to believe yourself and choose true. 7/9 overall, got the asymptote question and the not factorable questions wrong. I'm only in grade 8 so don't judge me, and I know some of you are going to say you are grade 6, ok, good for you.
So it’s literally impossible to get a 10/10
7/10 whitout any explanation, just guesses
(a+b+c)^2 _does_ equal a^2 + b^2 + c^2, _IF_ the following conditions are met:
1. Any one number is equal to the negative of the product of the other two numbers, divided by the sum of the other two products.
In other words, a = -bc/(b+c), b = -ac/(a+c) and c = -ab/(a+b)
2. No two numbers can be negatives of each other. I.e., you cannot have a 6, and a -6. The reason is that if you do this, then the denominator of the fraction used to find the third number will be 0.
Let's take two random numbers, 12 and 4.
Multiply these numbers to get 48, add these numbers to get 16, then divide 48/16 to get 3, then take the negative -3.
This gives us our 3 numbers, 12, 4, and -3.
These will be our a, b and c.
Or, simply put, if you take all 3 pairs of numbers, add them together, if the results is 0, then (a+b+c)^2 = a^2 + b^2 + c^2
Now, let's see:
(12 + 4 + -3)^2 = 12^2 + 4^2 + (-3)^2
13^2 = 144 + 16 + 9
169 = 144 + 16 + 9
169 = 169
So, yes it is true, but only for _specific_ values.
Very nice! I got the same results. The key was recognizing that 2ab+2bc+2ac could = 0 as you stated.
Very easy :)
I know how to get perfect marks. By presuming *you* got an answer wrong, then the last question can be answered to be false, which would be true.
So if I say I'm more right than you (like how my answer to question 3 was "PRINCIPLE ROOT CAN SUCK MY BUTT, I DON'T CARE, IT'S TRUE") and then say that the answer to question 10 is false, then I could've gotten perfect marks (if I didn't have a brainfart on question 4 from the amount of exclamation I had in response to question 3).
But then again, that requires circular logic,
so I might as well just say I got the test completely correct because beating the test means I'm smart and being smart made me beat the test and it'd be true because I said it which means it's true because I said it.
Part 2
If everyone guessed then 24 people should've gotten them all correct
I got 9 + i/10 (no.10 Is a paradox) (the final question is evil bruh)
I only got 5 (and 10 duh) wrong. Pretty good score imo but it still annoys me
8/9 for me who uasnt studied functions yet , so i didn't jniw what is asymptote
my score 5/10
I actually gets all correct 🎉
How ? You can’t answer question 10?
Sometimes, The Best answer is nothing. By not answering it, there's no reason for having it incorrect, and because "someone is inocent ultil guilty", because I don't have it wrong, I'm correct@@user-lu6yg3vk9z
I got (9.5土0.5)/10 :)
Of all the questions, i got the dlope one wrong.
This is just evil
7 out of 10 but 9th q is out of sllabus
9/9
I got ±5/10
9/10
9\10
8/10
I still dont get question 3, (-5)^2 does equal 25 so it is a solution
x² = 25 means x = ±5, and is denoted by ±√25.
Here √25 is the principal root which is greater than 0.
√ itself is a FUNCTION, which results in ONLY ONE VALUE (the principal root). In the case of a non-negative number, it returns a non-negative number.
-5 is a solution of x²=25 but it does not mean √25 includes -5. And it is also inaccurate to call √x "(the) square root(s)" of x. Instead we represent -5 as -√25.
Thats why we represent the "square roots" you stated as ±√25 instead of just √25, same as the ± in the quadratic formula.
Same as in cubic way, ³√1 = 1 while there are 3 roots namely 1, -½+√3/2 i and -½-√3/2 i, where 1 is the principal root and the other two can be seen by multiplying 1 by -½+√3/2 i once and twice respectively. Sometimes the constant is denoted as ω, then the three cubic roots become 1, ω, and ω².
And three cubic roots of 8 is then 2ω⁰, 2ω¹, and 2ω². So the ± thing in square root is just another way of writing its constant, -1, to generate other roots from the principal root.
Btw, the symbol ³√-1 has some ambiguity that the real cubic root of -1 is -1, while the principal cubic root is ½ + √3/2 i instead. (-1 = (½ + √3/2 i)ω). It needs to be defined when being used. But no matter how you define it, ³√ is still a function that represents ONLY ONE VALUE under a specific context.
@@twy_ exactly correct! great job!
I literally got 9 out of 10 only because no one has ever told me that asymptote is where the limit of f(x) at *x→∞* is
I got 3 of the 10 wrong
The answer to the last question is "or"
i got all of them right!
1. False.
(a+b+c)^2=a^2+b^+c^2+2(ab+ac+bc)
2. False.
sin(x+y)=cos(x)sin(y)+cos(y)sin(x)
3. False.
sqrt(25)=5
4. False.
A line perpendicular to y=5x has a slope of -1/5.
5. False.
A strictly increasing/decreasing continuous function can never touch an asymptote.
6. False.
The equation x^2+6x+25=0 has no real solutions.
7. False.
x^2+4 is not factorable without using imaginary numbers.
8. False.
sqrt(x)^2=x
9. False.
Applying the power rule of logarithms, as well as the product rule to log(3x^2) gives 2log(x)+log(3)
10. Bastud.
Well the last question Is both true and false otherwise I got a 7/9
Bro i'm not a high schooler
1. false
2. false
3. false
4. false
5. true (false)
6. false
7. false
8. false
9. n/a
10. why
yeah no, i'm too lazy to put the corrections ok
at first i didn't believe that no one had gotten 10/10 for this test and i thought he was arrogant then he got me with the question 10 paradox
im grade 6 and what the carp is this