[November SAT] The BEST SAT Math Trick
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- Опубліковано 17 жов 2024
- What’s going on y’all 🤙
This SAT Math trick will show you how to solve sat questions quickly and score higher.
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FAQ
Name: John
Where did you study - Emory University
What did you major in - Economics & Psychology
Can you tutor me - Contact me (john@admissionhackers.com)
How long have you been teaching - Since 2012
Why do you decide to teach - It was tough for me to figure it all out when I was in high school, and my goal is to make it a lot easier for current students
Can you make videos on Reading & Writing - I don’t know those sections well enough to talk about them.
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Matching Rule : ua-cam.com/video/yYeIFsby4tQ/v-deo.html
y=8 x=0
Bro the question you have is 9th grade level lmao even in 8th grade people know it.
Is sat this simple LMAO?
😂😂I quit got me
On the real projective plane, as long as the lines are different, there is always one solution. Two algebraic curves of degrees m and n intersecting on the complex projective plane will always meet in mxn points, up to multiplicities of intersections. (Bézout’s Theorem)
y = -3x + 8 and y = 3x + 8, both straight and not parallel, so one intersection.
That's how I did it, I prefer methods that are easier to visualize, because they're a lot easier to remember, even if it takes an extra few seconds to do.
and if you are really strugglign cant u just graph it and count?
That’s the same way I did it
@@mariam_ahI guess, but you would still need to simplify to get the “y” by itself
there’s only one solution since both intersect each other at the point (0,8)
Okay but you need to know this. You can't have 2 solutions for linear equations. It's always either zero, one or infinitely many. If the equations are identical, they have infinitely many solutions. If, they have the same slope, they have zero solutions. and if its neither, they have one solutions. Always automatically eliminate option 'two'.
you’re literally the only person who explained this with ease 😭
You are so smart
Great explanation!
exactly!
thx
Identical equation = infinite solutions
Same slope = zero solutions
Different slope = one solution
y cant u just solve it normally
@@smaransure2234 Well, you have to know how many solutions there are and this is just a trick to keep in mind so it is easier to know how many solutions there are. First, find the two equations for the graph and then use this method. Trust me, it is very helpful.
so what would be the slopes in this equation
@@Quixler
@@smaransure2234time
Quite helpful!
In the digital SAT, you have Desmos to use as you like. This is one of those questions that you simply plug into desmos and see if the lines are the same, parallel, or cross.
Wdym? Like desmos is in the computer you are doing the digital SAT on?
It’s included
@@promaster5533 Thanks
@@zencigaming
Its included in the SAT
One person on reddit solved almost all his SAT on desmos and got 790
Its OP
@@maarijfarrukh2019 send me the thread plz and thanks
I really wish they’d word these questions in a more clear manner. It makes it so easy when someone just tells me what the question is *actually* asking
How would you reword this question to make it clearer? It seems to be clear enough to me.
the point of the sat is to make easy math questions hard
This is not worded unclearly. If you find this hard, it is because you don’t understand the material
Two different lines that aren’t parallel will always only have one solution
That's right, but a line on top of a line segment are not parallel but have more than 1 solution.
Y+3x=8
2y-6x=16
Y = 8-3x
So we replace
2(8-3x)-6x=16
Then 16-6x-6x=16
Which gives us
0=12x
So x=0/12 so x=0
Then we plug it in to the first equation y+3(0)=8
therefor Y=8 and X=0.
So there’s one solution
¿Cero no sirve como solución?
@@marcosnead they only plugged the 0 back into the equation to check to ensure that 0 was a solution. A solution is only the x value, the y value just confirmed that the x value is true (it solves the equation).
u did not need to do all that just multiply top equation by 2, cancel the z’s ur left with 4y = 32 y = 8 so by then u know there’s just one solution so u got ur answer
cancel the x’s*
@@ritvikdevireddy8614there’s many different methods to solving equations like this, and some make more sense to others
Thank you so much. You are my saving grace. I have been having so much trouble with this. Even though I've taken a SAT class nobody has giving me a short and easy way to do these types of questions.
the E got me haha
😂😂 same
I quit… -me on SAT
I was taught to label each equation A B C ... The just create algebra out of those which you solve. Helps alot when you get 'are they skew?' questions.
y+3x = 8
2y-6x = 16
Multiply first equation by 2 to get
2y+6x = 16, subtract both equations to get
12x = 0. Solve to get x = 0
Plug in 0 to y+3x=8, y=8.
M=-m implies they are perpendicular meaning one intersection hence solution
You could just put both equations into the desmos calculator and see how many times they intersect, if they intersect once: one solution, if they dont intersect: no solution, if the lines are on top of each other (same line): then infinitely many solutions
Just make them slope intercept form and imagine it in your head. Like a rough shape you know
you can just put it in desmos and check at how many points the functions intersect
y + 3x = 8
2y - 6x = 16
Easy trick:
Since 16 is a multiple of 8 by a factor of 2 just multiply the entire first equation by 2.
Set the new equation equal with the original second equation and you get
2y + 6x = 2y - 6x
Next subtract 2y from both sides.
Now 6x = -6x
So just by plugging in a few numbers you should see that zero is the only number that fits.
I did that method too but I think what he did is a lil faster
Good job. At the -6x = 6x step, you can add 6x to both sides...then 12x = 0. divide both sides by 12 and x = 0.
@@Kawamata123 Nice way of finishing that!! Couldn’t think of a way to put a proof to the end!!
y+3x = 8 (1)
multiplying (1) by 2
2(y+3x) = 2y+6x = 2(8) = 16 (2)
2y - 6x = 16 (3)
adding (2) and (3)
2y + 6x + 2y - 6x = 16 + 16 = 32
4y = 32
y = 8
replacing y in (1)
y + 3x = 8
8 + 3x = 8
x = 0
thats how I would have wrote it in an exam, it's really easy to see in like 3 seconds
Just use substitution by elimination.
Multiply the top equation by 2, cancel out the x'es, and the add the two equations together. You'd get 4y = 32, so y = 8. Plug that back into any equation and x would make the equation true, making it one solution.
This is standard teachings on ninth grade algebra 1 so anybody taking the Sat's should know it.
You forgot to multiply the 8 by 2
@@KrebzonideWhat? Where do I have to do that?
@@armgrease When you multiply the top equation by 2 the 8 on the right side becomes 16. Add the two equations together and you get 16+16 = 32. I assume you missed the multiplication and did 8+16 = 24.
@Krebzonide Oh your right, sorry, I'll edit my comment.
We don't need to solve the equations to get the answer.
For ex:
The equations are in the form of
ax +by =c and a° x + b°y = c°.
So we just need to find the values of a/a°, b/b° and c/c°.
If
1) a/a°=b/b°=c/c° then the equations have infinite solutions as they are basically the same lines meaning they coincide at every point.
2) a/a° ≠ b/b° then the equations have one solution as they intersect at only one point.
3) a/a°=b/b° ≠c/c° then they have no solutions as they are parallel lines and never intersect each other.
So in this question,
a/a° = 1/2
b/b° = -1/2
c/c° = 1/2
As a/a° ≠ b/b° , the lines intersect at only one point thus they have only one solution.
If the equations are parallel (meaning they are shifted by a constance), the intersections will be 0. If the equations are identical, they share all solutions along the line, which is uncountable. If it intersects once it means the equations are neither of the above. These are the only possibilities, but if you’re running out of time just pick the 1 option.
Another thing to know is that you're working with two linear functions, which can only have 0 (parallel or same slope), 1 (for an intersection or different slopes) or infinite solutions (if both are the exact same function). Two solutions is impossible.
Why does SAT give the "I quit" option?😅😅
The x only has an exponent of one. The degree of the function is the number of solutions it has.
why do you have to complicate it? just try to visualise it in a graph in your head. It's zero if they're parallel, 1 if they're not, and infinite if they're the same line.
most students are HORRIBLE at visualizing! It's great that you can visualize but most students can't do it! So he isn't complicating it for the majority of students. His method is much better than visualizing!
@@gregoryharlston0602 I see. If you consistently use desmos, I think you'll get better at it.
Been taking linear algebra so Gaussian elimination was my first bet this neat
E) I quit...wow. 🤭😂🤣🤣
Two straight lines which are not parallel can only intersect at a maximum of 1 point. It cannot be infinitely many or two, and the equations do not have same slope with a vertical phase shift (no solution) so it must be one solution.
Takes like 1 second.
You are wrong about the first one, the criteria is that the ratio of coefficient of x and ratio of coefficient of y should not matching.
exactly
Just make the equations into slope intercept form (y=mx+b) then just imagine what those graphs would look like on a coordinate plane in your head and see how many times they intersect.
I’m in 7th grade and figured this out immediately, because if you think about it, 2y - 6x = 2y + 6x, making the only possible solution (0, 8)
Can’t we like do this on Desmos?
lmao desmos is so over powered I love it (collegeboard dont see this)
Wouldn't it be easier to multiply the first equation by 2 and add them? You'll get 4y + 6x - 6y = 32, so 4y=32, y=8, x is 0
By using inconsistency of the equations by using gassen
elimination method
This is a good introduction into the importance of linear algebra and the types of solutions you can draw from solving systems of equations, just wait till college-level introduces systems of differential equations, now that one's a doozy
OR...
open the provided desmos graphing calculator and plug in both equations. the intersecting point(s) will be listed.
Your welcome! 😁
Ok now i know for future video quiz
or, just put the two equation on the desmos and see how many intersections they have or not..?
Just put the two equations on desmos and see how much they intersect
Cramer’s rule in 2D basically
I'd do it like
y+3x=8=y-3x
3x=-3x
6x=0
x=0
and given that y +/- 3x = 8, y=8
This question was written directly in the class 9 NCERT.
It is literally in 10th standard linear equations in 2 variables
At my school I did these types of questions in year 10
This is something I learnt in 10th class
this is tough to derive though i would prefer to simply notice the second equation is divisible by 2, then put both in slope intercept form, and then notice they have different slopes and therefore intercept at one point
its obvious cant believe this comes in sat lmfao
a 9th grade question
Integrated graphing calculator goes crazy on these questions 💀💀💀
Can you use them during no calculator portion?
@@j_jayden0719No but these questions come up on the calculation portion
You dont need calculator to draw this graph its one of the easiest graphs to draw
Only solution is x=0 and y=8. Put x=0 so y=8 in first equation and 2x8=16 since x=0. The only one solution is possible by just looking at equations.
Or just plug in the first equation to the second and just getting the point of (0,8)?
that doesn’t guarantee it is the only solution, there could be infinitely many as well, namely scaler multiples of that solution
easier method put them in the demos calculator and see if they have any solutions
What if there is just 1 line, like x + y = 10?
OR, you could just put it into desmos :)
E is right 👍🏻
❤thank you🎉🎉🎉🎉🎉
I'm not convinced by this as your rule ignores the x coefficient. Surely the important thing is how x relates to y (the gradient). Since it's 2 straight lines if the ratio of x to y is the same in both equations they have the same gradient and so are parallel with no intersections. In this case they don't have the same gradient so there is one intersection. Alternatively rearrange into the form y = mx + c to check if the gradients are the same. Your answer is right but your method doesn't work.
Can’t you just use elimination?
Simultaneous equation
I just took linear algebra so my brain just ran through it in matrix form.
Bro it can be solved in less than 15 seconds. Multiply the first equation by 2 and then you would realize its different slope so its one solution.
Hi, I want to buy your course but the thing is that I'm a foreigner ",i have never taken sat before and my math score is 250 and you said your course can help only students who have above 400 points
Should I purchase your course
If not how can I improve my score
Thanks!
Well now because you have Desmos you can just put the equations in it and find the answer
I mean... You could just punch it in ur gdc. Or just look at the equations. They are straight lines. So ofc only one intercetion
what if none are matching
Can we use demos calculator?
What if The x portion and number portion are matching
What about 2 ?
Thank you! '
The goat
Ayo, you sound like Sal from Khan 👾
x=0,y=8. It's over.
Too good
Thank you!!!
Just put the equations on a graphic calculator. You can literally see the nnumber of intersection points
you cant do that on sats lol
It's a just a freaking equation of 2 lines ,either they intersect each other at one point or they don't when they are parallel, you don't even need to lift your pen🫡
Bruh theres same equatio. Too
i feel the pain, bro, work like 100x for jee and you get to mit solving these questions@@sysylaelhip5240
Just use the DESMOS?
For linear equations , we will be having only 1 solution for each variable.
how do you get these questions
F) Use Desmos
Just use desmos to graph
This is sats?
thx
So what should be matching for 2 solution?
It's not possible for a system of linear equations to have exactly 2 solutions. That requires a non-linear system, usually one that reduces to a quadratic. In fact, I'd expect that all examples that do have 2 solutions you'd get on the SAT's, will ultimately involve quadratics in some form or another.
Granted, there are examples with 2 solutions that have nothing to do with quadratics, like x*2^(-x) = 1/4, but these are uncommon for high school level academics. This one in particular requires the LambertW function.
or just plot it on desmos and see how many places the two lines intersect..
what is SLAP sir in graph question
Here's what I did:
y + 3x = 8
2(y + 3x) = 16
2y + 6x = 16
2y + 6x = 2y - 6x
6x = 0
So y = 8. x = 0. Answer is 1.
fundamental theorem of algebra says one
desmos?
So simple
But the problem you solved all of them were the same so isn't it infinite solutions??
If there are infinite solutions, it ultimately means that they are the same equation, just a scalar multiple of each other. Redundant equations.
If there are no solutions, it means they are contradictory equations.
Two linearly independent equations in a linear system, will have exactly one solution.
What if you have none matching?
Choice E
Dude it’s two lines unless it’s parallel how would there be more or less then one intersection it doesn’t have exponents
Playing devil's advocate:
Trigonometry doesn't have exponents, and you can have lines intersecting trig functions that have 2 solutions.
how to never get it wrong... use desmos
Why can't you just solve it normally by eliminating a variable, and if they're parallel, both the variables will be eliminated
Because you don't need to. A simple inspection is all that is needed.
@@carultch idk why the hell i typed this comment when i knew how to do this just like the way he did in the video
Although a better trick would be to just match the slopes and clearly they're not equal so it's 2 solutions, if they were equal then we would have to check using coefficients
I''ll just use Desmos
How the hell is Desmos allowed on the SAT?
Why tf would you possibly do it this way? Memorizing "rules" like this without emphasizing why is partly why we have so many mathematically illiterate people.. smh
If you draw two lines you get 3 possibilities: they either intersect ones, infinitely, or never
They intersect once if the slope (or the amount of tilt) is different.
They have infinite solutions if it’s two equations for the same exact line (the values in the simplest form are the exact same)
They have no solution if the lines have the same slope but start at different points.
To make it easier for yourself learn how to turn the equations into a standard linear equation (y = mx + b (where y is alone on one side of the equation)) if both equations have the same “m” but a different “b” then it has no solution, if “m” and “b” are the same then it has infinite solutions, otherwise it has only one
Bruh just use,
• a1/a2 = b1/b2 = c1/c2 then its infinitely many solutions
• a1/a2 ≠ b1/b2 then its one solution
• a1/a2 = b1/b2 ≠ c1/c2 then its no solution
Solved in seconds by this method.
How do u find a1 b1 and everything else?
@@autumnsky4220 They are coefficients of x1,x2,y1 and y2.
@@adaaaa6642 ohhhh thxx
Btw, what is the c? Is it the y?
@@autumnsky4220 It is the constant.
We get such qs in class 10 bro 😂
Or just use the desmos on the digital sat
E?
Desmos question next