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This is how SAT likes to ask "weird symbol" question. Redddit r/HomeworkHelp
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- Опубликовано: 25 апр 2024
- This is a class way that the SAT likes to weird symbol operation questions. This question is from Reddit r/HomeworkHelp / fpowtxbrhe
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#math #algebra #mathbasics
x∆ is really just another way of saying f(x)
f(x) = (x-1)(x+1)
Yes.
and a stupid one while we're at it :)
Thanks for this clarification. I was confused about this because I thought you were supposed to solve for the triangle🤣.
Seeing that as a programmer, it seemed so obvious that the triangle was just another way to say "this represents a function". It's like in programming- if you're going to use this equation a lot, you'd be better off just making it a function and calling that with your value! I bet you could use any non-mathematical symbol for that, like a square or a circle, and it'd still be valid. I guess the triangle is just a convention due to delta already being a mathematical term?
@@NimonoSolenze: Since Δ already has a meaning in math that's _different_ from this meaning, that makes it a particularly _poor_ choice. Although making it a solid ▲ mitigates that.
i just saw it as a difference of squares, so it's x^2 - 1 inst of (x - 1)(x + 1). saves calculation, as only substituting once.
me too
Much easier to do in your head, and quickly with fewer mistakes, that way
it's easier if you unfactor it and just say it's just x^2-1. So it's 36-1-(25-1) and then it's also easier to find out which answer is the same as 11.
I received a Ph.D. at a major university and went on to help a Fortune-500 Company make a lot of money. It's a good thing I was never required to take a SAT exam or I'd probably still be scrubbing pots and pans at our local restaurant.
PhD major??
@bdulAhad0 that is not what he said...
Bro you make no sense
(x+1)(x-1) = x^2 - 1, which makes the whole thing a lot simpler as you can immediately rule out A, C, D and E, leaving .... B.
This is the right way to approach it. If you do all the calculations the "right" way you will run out of time. You have to get into the question writer's head and figure out how to do it super quick
Haven't seen the whole video yet, let me try...
Denoting with f(x) = (x-1)(x+1),
f(6) - f(5)
= (6-1)(6+1) - (5-1)(5+1)
= 5×7 - 4×6
= 35 - 24
= 11
■
(Ain't no way that's 10th grade algebra...)
In my generation, it was extensively taught in 10th grade. The concept is already taught in 8th grade however.
What interpretation of the given equation would be that the triangle is another variable, so the initial equation would be like XY = (x+1)(x-1), and so arguably the Y (triangle in other words) would equal X + 1/x ? This makes none of the answers valid I don't think, but I feel like that shouldn't be the only motivator. Maybe the setup precludes this interpretation, though?
(x+1)(x−1) is x²−1, so 6▲−5▲ = 6²−5² = 11 (the −1s cancel). We want to express this as a▲+b▲, which is a²+b²−2, so express 13 as a sum of squares. And since I memorized all of the 13-partners a long time ago, I know immediately that that's 4+9. So it's 2▲+3▲.
I always found it funny when I was in SAT Prep class in high school and a large portion of the class was learning about how the SAT makes questions tricky/confusing to make it more likely for you to make a mistake even if you know what you're doing
This is a perfect example of this where they use "x∆" instead of "f(x)" since they're trying to throw a symbol at you that you don't know and make you second guess if you really know what you're doing or not. They also decide to make the answers in the "x∆" format to add an extra layer of confusion onto the question since it's basically saying "compute 6∆ - 5∆ and then figure out which of these other x∆ equations has the same value"
Imagine how much better people's SAT scores would be if they gave 100% straightforward questions only using notation learned in class. Even when I was in college-level math courses, they only used standard notation learned in high school and didn't try any "x∆" nonsense on us
I was a foreign exchange student in the USA in 88-89, took the SAT, scored +99% on it (I don't know if it still gives percentages nowdays). Had one mistake because the numerical score was 20 points less than maximum, if I remembre correctly (580/600 or something like that). I know exactly where I missed the answer,.
The question was x^2-9=0, and the answers were given as:
a) x=3
b) x=-3
c) x=0
d) none of the above
and I've spent at least 5 minute son that one, as the correct answer is x=+-3, so it wasn't given, but also it is in two of the above answers, thus not in "none of the above". The answer thus became not a mathematical one but a semantical one, and finally I decided to check a) x=3 as I didn't know whether Americans even learned that when you're looking for a solution of x there are two answers, whereas when you're looking at purely calculating then it's only the positive one. This decision was also due to knowing that kids in school around me were quite bad at math, so I concluded that most likely they were not taught correctly. Well, my mistake :D
If the SAT only gave "100% straightforward questions," it would only test people's ability to do things that they had explicitly been taught how to do, and not their ability to think and figure things out.
If you take college-level math courses, chances are you're going to encounter symbols you haven't seen before (sometimes only defined in a specific context), and you'll have to understand how they work based on the definition you're given.
@@Steve_Stowers There's a big difference between having people "think & figure things out" and senselessly throwing confusion into the question by using unconventional notation
On one hand, you have the SAT question that intentionally uses "x∆" when "∆x" would make it a delta-based question with a completely different method of solving and different answers
On the other hand, you have nice questions that BPRP poses such as a question from 10 days ago where he shows you how to factor a 5-term 4th degree polynomial expression that really gets you thinking outside of the box, BUT in a way that actually challenges your math skills and not in a way that tries to trick you with unconventional formatting
While some people who have English as their non-native language may not be phased much like @z000ey, that isn't the case for everyone. If you have native English speakers who end up stumbling on questions that use unconventional formatting/structure, then it would only be natural that a non-native English speaker would statistically be more impacted by this decision for SAT tests
Basically, they want to challenge you with reading comprehension (I thought there was an English part of the test for that???) instead of your mathematical skills in order to cause you to make a mistake you wouldn't have made if it was using proper notation
@@TheZeevil The way I see it, the ability to accept and work with newly-defined or unfamiliar symbols and terminology IS a key mathematical skill. I assume they used the solid triangle (which, being solid, is not a delta) as a symbol precisely because they wanted something that didn't already have a predefined meaning that some test-takers would be familiar with.
From the point of view of test designers, the purpose of any test is not to make scores as high as possible; it's to accurately assess what the test is intended to assess. I think where you and I disagree is over what we think this question is, or should be, trying to assess.
have to justify the price of themselves. and the absurd prices they charge.
while testing for the ability to adapt is good, this isn't their intention.
what a ridiculous question
This is much more common on the CLT test. Have not seen this during SAT training.
Clear as mud.
XΔ - YΔ = X^2 - Y^2 and XΔ + YΔ = X^2 + Y^2 - 2
we are 6Δ - 5Δ = 36 - 25 = 11
Check middle of proposals: 4Δ + 3Δ = 16 + 9 - 2 = 23 (Too large, so the other proposals below will also be, no need to check.)
Check the one above: 3Δ + 2Δ = 9 + 4 - 2 = 11
The first will also be too small, no need to check.
Answer: 6Δ - 5Δ = 3Δ + 2Δ
One Doubt here,
Shouldn't,
X(Triangle)= (x-1)(x+1)
Be
Triangle= [(x-1)(x+1)]/X?
no, triangle here isn't a variable, it's an operation you're doing on x. it's the same as a function f(x) = (x+1)(x-1), but with a funny notation (xΔ)
No, Δ here is like an operator on x, just like the nabla operator ∇.
@@duccline ohhhhh, thank you for explaining. 🙏
Ehhh.. you got a new phone cover
They put empty triangles instead of empty boxes
You gotta fill the triangles with numbers
Anybody else notice the title says "redddit"?
10 minutes ago is crazy
tests abstract thinking which, if i am not horribly mistaken, is not taught at all in the US
Man, I am so glad I took the ACT instead.
But there's a way to find the answer without guess & check?
(x+1)(x-1) = x^2 -1, so we have 6^2-1 = 35, and 5^2 - 1 = 24, 35 - 24 = 11
All of the options A-E are sums, so you can immediately rule out any that have any number that squares to greater than 11 (C, D & E) and any that could never get there ... which is A
This leaves only B as a possible answer.
@@Kyrelel Thanks!
Is this a cultural thing? I got my math education in Germany and have *never* seen this notation.
It’s more of a style of asking the question. They can define anything anyway they want. Such as x# means x^2-3x. Which is just another way to say f(x)=x^2-3x
@@bprpmathbasics OK. Like I said, I've never seen this before.
I guess, as long as the SAT examinees know what it means it's no problem. 🙂
I appreciate the feedback!
These are Gaussian Integers, aren't they?
Gaussian integers are a classification of numbers, that are complex numbers made up of integer components in cartesian form. So not only are these Gaussian integers, these are ordinary integers as well, since imaginary numbers aren't involved.
This is disrespectful to Euler