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The only SAT Math DESMOS Guide you'll ever need

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[Music]

Nothing in life is certain except death

and the uh Desmos calculator on the SAT

this calculator is actually a godsend

but most people don't know how to use it

including KH Academy themselves which

still tells you to solve every single

Problem by hand I love you s but this is

stupid Desmos is fast and Desmos is

accurate and in this video I'm going to

tell you exactly how to use it and so do

not let your Zoomer brain get distracted

unlike my fellow sat YouTubers I'm not

going to put you to sleep this video is

fast it's efficient and it's going to

help you improve your score so Now's the

Time to lock in the first thing you want

to know is that the Desmos desmos.com

calulator is pretty much the exact same

version that you'll get on the SAT the

only differences are you can't upload

images sure and you can't uh Play Sounds

which I'm sure is disheartening for most

of you okay now on to single variable

equations most people are sheep and

they're going to solve this problem by

moving X plus 6 to the other side

subtracting by 55 Distributing factoring

splitting up rearranging and picking the

positive solution but Sigma males like

myself are just going to copy and paste

it into Desmos and look at where the

vertical line is so even if you have no

idea how to do any of this as long as

you know how to use a keyboard you

should be able to solve any single

variable equation on the SAT whether

it's a square root equation or an

absolute value equation or a rational

equation or a quadratic equation or

t okay hold on guys remember I'm a sigma

male I've got this uh this question is

asking for when there are no real

solutions so I can just replace t with

all of the possible answer choices and

then see which graph doesn't show any

solutions and that's the correct answer

I know guys I know hold your applause

systems of equations you're never going

to guess what you do for

these plug them in asmos that's right

baby we're going to Harvard now if you

want to get technical you can think of

the red line as every single point that

satisfies the first equation and the

blue line is every single point that

satisfies the second equation so the

point of intersection is the only point

that satisfies both equations this works

for quadratics too as long as there are

two equations and two variables you can

find their point of intersection

sometimes there might be multiple points

of intersection like in this goofy

system now you may realize that every

single variable equation can be

Rewritten as a system of equations and

vice versa for example let's say we have

this single variable equation right here

with Solutions 2 and 7 if we wanted to

express this as a system you can set y

equal to the left side of the equation

and y equal to the right side of the

equation notice that the quadratic and

the line intersect at x = 2 and x = 7

which were our two solutions and so for

the SAT you should have a conceptual

understanding of solutions you should

understand Solutions in the context of

systems of equations like this and you

should understand Solutions in the

context of single variable equations

like this and you might be thinking well

yeah I see how they relate but when

would I ever want to convert one into

the other well look at this problem if

we plug it into Desmos it seems like

there's no solution right this is just

like that one problem from 2 minutes ago

with the constant but if you split this

up into a system of equations you'll see

that these are actually just the same

line and a line intersects itself

infinite number of times therefore there

are actually infinite solutions not no

Solutions so be warned when doing what I

did 2 minutes ago because no Solutions

and infinite solutions of a single

variable equation look the exact same

okay side tangent that has literally

nothing to do with the SAT Math I bought

this green t-shirt off Amazon to try to

use as a green screen but my editing

software doesn't like it so it's just

this comically bad green screen but at

least I only bought one t-shirt am I

worse just like systems of equations you

can solve systems of inequalities just

by plugging them straight into Desmos

Desmos will shade the regions that

satisfy each inequality so for a problem

like this where you're trying to find a

solution you don't need to look for the

point of intersection but rather any

point where the red and blue regions

overlap in that case this would be 140

now the SAT might ask questions that

give you an in quality in context so in

this scenario we're buying apples and

bananas but we have a price constraint

and a quantity constraint and price and

quantity constraints are a very common

problem type you'll see on the SAT and

this question is not just asking what is

a valid point for this inequality it's

specifically asking for the maximum

number of bananas so the way we would do

this is first we' want to graph our

inequality we can't use A's and B's cuz

Desmos thinks those are constants so we

have to use x's and y's so you can think

of every single x coordinate as the

number of apples we're buying and the

y-coordinate as the number of bananas

we're buying so for example this point

right here means we're buying four

apples and two bananas and you can think

of the green region as every combination

within our budget and the black region

as every combination where we're buying

at least six fruits and we're interested

in the overlapping region where we're

simultaneously staying within our budget

but also buying enough fruit and we're

trying to find the most amount of

bananas we can get while being Within

this overlapping region in this case

bananas are y so we want to take the

greatest y within our region which is

going to be 10 and you might be thinking

well aren't there a lot of numbers

greater than 10 like we're still in the

Shaded region when we're at y = 12 or Y

= 14 or yal 16 but look at what happens

to X our X has to be negative for us to

buy more than 10 bananas that means

we're buying -3 apples to pay for our 16

bananas you can't do that you can't just

just walk into the store and be like

I'll take -3 Apples please um to finance

the rest of your purchase so just

because the graph seems to indicate

something doesn't mean that you can

ignore the context of the original

problem but students do this all the

time the question will ask for a

positive solution and they'll pick the

negative one the question will ask for y

and they'll pick X don't get lost in the

sauce and remember what you're actually

solving for this is just general sat

advice by this point of the video if you

are not already sold on how fast and

easy Desmos is let me prove it to you

I'm going to show you how many problems

can be solved in just one minute using

Desmos while I talk about today's

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[Music]

subscription okay next up quadratics if

you don't know what a quadratic is it's

a function where the highest powers to

and graphically it makes a parabola like

the St Louis Gateway [Music]

[Music]

Arch actually I'm mistaken this guy

wrote a 10-page paper on why the St

Louis Arch is actually not a parabola

Jesus Christ the point is quadratics are

incredibly common on the SAT and Desmos

is very much your friend anytime you're

asked to find the x or y intercepts of a

quadratic just plug it into Desmos and

click on the intercepts there you go and

by the way you can do this for other

functions too it's just that those are

usually easier to do by hand then

there's the vertex of a quadratic the

vertex is basically the end of a

quadratic it's the minimum or the

maximum and it's very easy to find if

you plug the quadratic into Desmos and

then click on it that's it now what if

they try to Spook you this problem isn't

just asking for the minimum of f ofx

5 people said I use the vine boom too

much so I've replaced it with gong Sound

effect. MP3 I think it's an improvement

okay back to the problem finding the

that's right it grabs the translation

for you this is crazy you can also do

this for any other sort of

this okay buckle up this next question

is important in the XY plane the graph

of the equation Y = x^2 + 9x - 100

intersects the line yal C at exactly one

point what is the value of C so we graph

our quadrant and our line into Desmos

and for some reason it treats c as a

variable rather than as a constant so

rewrite c as 0x + C and then you can add

the slider but wait our C slider doesn't

bring our line all the way down to the

quadratic so we need to click on our

lower bound over here and set it to

something much lower like 100 so now we

can bring our line all the way down to

the quadratic but if we zoom in we'll

see it's not actually touching the

quadratic when it's at -80 it's one too

low and when it's at -79 it's one too

high so instead let's manually input all

four answer choices into desos -41 over4

um nope that's not touching -00 nope

that's not touching NE - 319 over 4

there we go but this seems much longer

and more tedious than it should be if we

acknowledge that the point of

intersection is the vertex of the

quadratic then we don't even need this

line we can just graph our quadratic

click on the vertex and that's our

answer -

79.7 is -39 over4 the reason I went

through this whole laborious process is

that this is what most of my students do

and I want you to avoid this mistake

when there is one solution or one point

of intersection between a quadratic and

a horizontal line it's at the vertex

don't forget that now you might get

unlucky and college board just gives you

a problem where the line is not

horizontal at which point you kind of

have to plug in every single answer

choice but most of the time the line's

going to be horizontal and all you're

vertex in this problem we're given a

quadratic equal to zero and told the

equation has no real solutions when C is

greater than n the easiest way to think

about no Solutions is with a system of

equations so we want to do what we did

earlier in the video and split each side

into its own equation now the question

becomes simpler it's asking what does c

need to be greater than for our

quadratic to be above the x-axis so we

drag our C until the quadratic reaches

the x-axis and see that any value above

289 is above the x-axis therefore 289 is

our answer if it doesn't make sense what

I'm doing go back through this section

and try it yourself I'm going quickly so

I don't have to make 19 videos about

this but if you actually want to

internalize this stuff you need to

practice and think through these

problems on your own now here's the

catch with problems that ask about no

Solutions if there are no solutions for

a system with a quadratic use Desmos if

there are no solutions for a system of

linear equations do not use Desmos for

example take this problem you're given

two lines and asked if the system of

equations has no solution what is the

value for a well if two lines have no

solution that means they never intersect

if two lines never intersect that means

they're parallel if two lines are

parallel they share the same slope I

like to think of this as two cars

traveling one behind the other if

they're going the exact same speed

they're never going to crash just like

how two lines that increase at the same

rate are never going to intersect so

this question is very simple we just

want the slope of the second equation to

be the same as the slope of the first

equation so a equal 2 even if you get a

harder variation of this type of problem

you can rearrange it into slope

intercept form and then set the slopes

equal to each other and yes you can go

into Desmos and move your slider around

until the lines are parallel but this is

very imprecise and you're too likely to

make an error so again use Desmos for no

solutions to a quadratic use paper and

pencil for no solutions to a system of two

two [Music]

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lines okay this one's just funny to me

you can literally type median followed

by your data set in parentheses and

Desmos will give you your median it's

the same thing with mean it's as simple

as that the thing is college board knows

this so for every stupid easy mean and

median problem they'll give you one of

the hardest problems on the entire test

so if you're trying to get a say 700 or

higher you still need a strong

understanding of mean and median but for

the rest of you you kind of just plug it

in so for the rest of this video I'm

going to be covering topics that are a

little more ambiguous on whether or not

you should be using Desmos some tutors

will say you should some tutors will say

thoughts functions are weird in theory

you shouldn't need Desmos for a problem

like this if you're decent at algebra

and arithmetic you can do the math

pretty much in your head but if you're

the kind of person to mess up 56 divid 7

then Desmos is probably more reliable

you can treat functions like single

variable equations simply replace n with

X set the function equal to 56 and then

you get your value for n as a vertical

line same thing with this problem where

you're turning a function into a table

you shouldn't need Desmos but it doesn't

hurt you can go to this plus sign and

add a table and then for your table set

your first column to X and your second

column to x uh 2x^2 + 9 so then we can

input our values - 1 0 and 1 because

that's what our answer choices have and

it'll automatically populate the other

side of the table so we can select

answer Choice

a I've seen plenty of people use Desmos

to make circles but most Circle problems

on the SAT are really just testing if

you know the circle formula like this

problem if you know the circle formula

you can clearly identify your Center and

radius in less than 5 Seconds so

learning your circle formula should be

the priority however there are problems

like this one below where you're told AB

lies on the circle and asked which of

the following is a possible value for a

this is basically asking you which X

values on the circle and if you graph

the circle in Desmos you can clearly see

that the circle goes from -15 to 7 which

means -14 is the only possible x value

so some circle problems are better with

you know it's an equivalent expressions

problem when it asks you which

expression is equivalent to this and

this is definitely not a problem type

you should use Desmos for is it

technically possible yes is it

optimal no please for the love of God

just learn how to factor and do Algebra

it comes in handy on so many different

parts of the SAT so just learn it and

get used to it the greatest common

factor of this expression is X so the

answer is the one that factors out X

it's that simple you don't need to plug

in every single answer choice to figure

that out you just need to give it 5

Seconds of thought and so to summarize

everything from this video you should be

using Desmos 4 single variable equations

systems of equations systems of

inequalities number of solutions x and y

intercepts vertices of quadratics

quadratics that intersect the line at

one point quadratics that intersect the

line at zero points Computing mean and

median directly and finding valid points

on a circle you should not use Desmos

for linear systems of equations with no

solution mean and median problems that

aren't literally just finding mean and

median finding the center or radius of a

circle equivalent expressions or

literally anything else on the SAT if

you found this video helpful please like

And subscribe and if you're interested

in private tutoring from me personally I

know crazy you can go over to learn sat

math.com in book of session I've been at

this for 3 years now I really know how

to teach this test and I've helped

countless students improve their scores

thanks for watching and good luck studying

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YouTube Transcript:
The only SAT Math DESMOS Guide you'll ever need