Part 1: Use Desmos to Ace the SAT
Summary
TLDRThis video tutorial explores the use of Desmos, a powerful graphing calculator, for solving various questions on the digital SAT. The presenter begins with a basic introduction to Desmos, demonstrating how to graph equations, adjust settings, and utilize features like sliders for dynamic visualization. Through a series of SAT problem examples, including linear and quadratic equations, the video showcases how Desmos can simplify the process of finding solutions. It emphasizes the importance of understanding Desmos' functionality to efficiently tackle SAT questions, providing viewers with practical tips and strategies to enhance their test preparation.
Takeaways
- 💻 Desmos is a powerful graphing calculator accessible online at desmos.com, offering a user-friendly platform for graphing various equations.
- 🔢 You can easily graph basic functions and equations by typing them into Desmos, such as linear equations and quadratic functions.
- ✍️ For exponentiation, use the shift key and the number 6 to enter exponents in your equations, facilitating the graphing of polynomial functions.
- 🖋️ Desmos allows the addition of multiple functions in one graph, with each function automatically assigned a different color for distinction.
- 📚 The settings menu (gear icon) in Desmos offers customization options, including changing graph colors and adjusting grid visibility.
- 🔍 The 'Home' button quickly resets the graph to its default zoom level, making it easy to return to the original view after exploring different parts of the graph.
- ⚙️ Advanced settings enable manual adjustment of axis ranges and steps, enhancing the visibility of specific graph features according to user preference.
- 🛠 When inputting equations from the SAT into Desmos, removing '=0' might be necessary for the graph to display properly.
- 🔄 Desmos' slider feature allows dynamic exploration of how changing parameters affect the graph, aiding in solving equations with variables.
- 📝 The tutorial emphasizes the versatility of Desmos in solving a variety of SAT problems, including systems of equations and quadratic equations, by visualizing and manipulating graphs.
Q & A
What is Desmos and how can it be used for the digital SAT?
-Desmos is a graphing calculator accessible online at desmos.com. It can be used to solve mathematical problems, such as those found on the digital SAT, by allowing users to input equations and visually see the graphs generated from those equations.
How do you graph a basic function, like 3x minus 5, on Desmos?
-To graph a basic function like 3x minus 5 on Desmos, simply type the equation into the input field. Desmos will automatically graph the line corresponding to the equation.
How can you adjust the exponent in an equation on Desmos?
-To adjust the exponent in an equation on Desmos, press the shift key and then the six key (which has the caret symbol '^') to enter the exponent mode (superscript), then type the desired exponent number.
What is the process to change the color of a graph on Desmos?
-To change the color of a graph on Desmos, click the settings button (gear icon) next to the equation you wish to change, then click on the color option and select the desired color.
How can you reset the zoom to the default setting on the Desmos graph?
-To reset the zoom to the default setting on the Desmos graph, click the home button located near the graph area. This will return the graph to its original zoom level.
What should you do if typing an equation exactly as it appears on the SAT into Desmos does not generate a graph?
-If typing an equation exactly as it appears on the SAT into Desmos does not generate a graph, try removing the '=0' part of the equation. This often resolves the issue and allows the graph to be displayed.
How can you add a slider for a variable in Desmos and what is its benefit?
-To add a slider for a variable in Desmos, input an equation with a variable (e.g., c) and Desmos will prompt you to add a slider. This feature allows you to dynamically adjust the value of the variable and see how the graph changes in real time, which is useful for visualizing the impact of different variable values on the graph.
What is a common workaround for graphing equations that don't directly support implicit equations of x and y on Desmos?
-A common workaround for graphing equations that don't support implicit equations of x and y on Desmos is to add a term involving x that doesn't change the equation, such as adding '+0x' to the equation. This allows Desmos to process the equation.
How can Desmos be used to find the intersection point of two graphs?
-Desmos can be used to find the intersection point of two graphs by graphing both equations and using sliders to adjust variables, if necessary. This visual approach helps identify the point(s) where the graphs intersect, which is particularly useful for solving problems involving systems of equations.
Can Desmos solve simple algebraic equations, and how?
-Yes, Desmos can solve simple algebraic equations by graphing the equation. The point where the graph crosses the x-axis represents the solution to the equation, allowing users to find the answer without manually solving it.
Outlines
📊 Introduction to Desmos for the Digital SAT
The video begins with an introduction to Desmos, a graphing calculator accessible at desmos.com, highlighting its use for answering questions on the digital SAT. It covers basic functionalities, such as graphing linear and quadratic equations by typing in expressions directly and adjusting their appearance on the graph. The presenter explains how to use the shift key for exponents, add new functions, change graph colors, reset zoom with the home button, and modify graph settings like axis steps and grid lines for clearer visualization. The segment emphasizes the importance of familiarizing oneself with Desmos to efficiently solve SAT questions.
🔍 Troubleshooting Graphs and Leveraging Desmos Features
This section deals with troubleshooting issues when graphing equations directly from the SAT on Desmos, such as removing the '=0' from equations to display the graph. It demonstrates using Desmos to solve a specific SAT question about finding the value of a constant 'C' where a line intersects a parabola at exactly one point, showcasing the utility of sliders for changing variable values dynamically. The presenter shows how to adjust the slider range and step to find the precise value of 'C' for the intersection, emphasizing Desmos's capability to visually solve equations and the strategy to include necessary terms like '0x' for equations lacking an 'x' term.
🛠 Advanced Graphing Techniques for SAT Problems
The video progresses to more advanced uses of Desmos for solving SAT problems, including adjusting slider steps for more accurate solutions and demonstrating how to graph implicit equations by adding terms. It solves another SAT question involving the intersection of a parabola and a line to find a specific value, highlighting the need for precision in adjusting the slider for accurate intersection points. The explanation covers how to interpret Desmos's error messages and modify equations to meet its requirements, illustrating the platform's versatility in handling various mathematical problems.
🎓 Practical Examples and SAT Strategy with Desmos
In the final part, the presenter uses Desmos to solve additional SAT questions, focusing on equations involving quadratics and systems of equations. This includes tips on using sliders for variables and interpreting the graphical results to find solutions. The video also touches on solving equations directly in Desmos without algebraic manipulation, showing how the graph intersects the x-axis to reveal solutions. The conclusion offers study tips, encourages viewers to explore further Desmos resources, and invites feedback for future video topics, underscoring the tool's value in preparing for the SAT.
Mindmap
Keywords
💡Desmos
💡Graphing
💡Digital SAT
💡Functions
💡Sliders
💡Quadratic Equations
💡Intersections
💡Coordinate Plane
💡Zoom and Settings
💡System of Equations
Highlights
Introduction to using Desmos for the digital SAT
Overview of Desmos' default screen and basic functionalities
How to graph basic functions and create exponents in Desmos
Adding multiple functions and changing their colors for differentiation
Resetting the graph to default zoom and modifying grid settings
Adjusting axis scales and steps for detailed graph views
Troubleshooting graphing issues with equations equal to zero
Solving an SAT question on graph intersection points using Desmos
Utilizing sliders in Desmos to find specific values in equations
Exploring Desmos' keypad functionality for equation input
Demonstrating how to solve quadratic equation problems with Desmos
Using Desmos to find the number of real solutions in quadratic equations
Applying Desmos for system of equations to find specific intersection points
Clarification on interpreting Desmos results for SAT question answers
Showcasing the versatility of Desmos in solving a variety of SAT problems
Conclusion and encouragement to use Desmos as a study tool for the SAT
Transcripts
hey guys in this video we're going to
look at Desmos and how we can use it to
help us answer some questions on the new
digital sat
[Music]
[Applause]
so on the right here on my screen you
could see if you've ever used Desmos
this is the graphing calculator
and you could access it if you want to
just play around with it on your own you
could go to desmos.com calculator of
course you could just Google it you'll
find it easily but this is the kind of
the default screen that you come to when
you're on Desmos and before we get into
solving some questions from the SAT
let's just talk about some of the
functionality
components to Desmos that we're going to
need to know so of course you can just
kind of type in whatever you want 3x
minus 5 and you can see that that line
3x minus 5 is graphed there
if you want to do an exponent like if I
want to make it 3x squared I can hit the
shift key on my keyboard and then I can
hit the the six key which is like the
little up arrow thing which I'm sure you
know how to do an exponent but that's
how you do it so shift and then six and
it goes to that what's called a
superscript and you could put a 2. so 3x
squared and then if you just like hit
the right arrow from here it'll
go down back to the normal level so 3x
minus 4 maybe is that okay so that's how
you just kind of start with graphing
some basic functions in Desmos if you
want to add a new function you could
just click down here on the second line
down
and you could put in another function
like y equals 4X minus 1. and there's
that and you can see that the the graph
automatically changes to a different
color typically
um you could change it if you want I
don't know why you would care to do that
but you could hit the settings button or
that little
um what do you call that yeah the gear
and then you could click the color and
you could change it right and it changes
from green to Orange to whatever the
heck you want it to be okay but that's
not that that important if you scroll
you could scroll by dragging obviously
that's easy but if you want to get back
to the default Zoom of this graph you
could just always hit this home button
here and it'll go to the default which
was right there okay so that's helpful
if you're zooming out really far to see
a graph that's not anywhere close to the
origin and if you're maybe scrolling
like this and you need to just quickly
get back to the start you just hit the
home and it resets everything which is
really really nice
now another thing that you can do is if
you hit the the wrench there you can
change the settings so if you you know
just play around with this if you want
but if you don't want those little grids
grid lines you could uncheck that and
you could kind of see in the background
there it makes those disappear
um you could change the x-axis and the
y-axis so maybe instead of zooming it
with the zoomed in plus sign and zoom
out minus sign if you want to manually
change how far the x-axis goes or the
y-axis you can change that here you
could even change the step of the axis
so watch this is maybe important enough
to to really talk about so if I zoom in
notice that you can't see you know one
two three four all you see is zero and
then five is the next number but that
would be changing the steps so if you
check the wrench here click the wrench
you could change the step to one and you
could change the y-axis step to one and
that way you could see all the numbers
and if you don't want those little grids
grid lines you could Click Of course
like we already said uncheck the minor
grid lines and this is kind of a nice
way to see
the graph so I prefer that of course you
could do whatever the heck you want if
you zoom it out it makes them disappear
but you get the idea so that's kind of
the the basics of Desmos the other thing
that I should mention is sometimes when
we see equations on a on the SAT like if
we look at this second one down here 64x
squared plus BX plus 25 equals zero
don't worry about the B for now but if
we were going to type that into Desmos
and let's maybe even put a a number in
in place of that b so if it was
something like 64 x squared whoops I
totally messed that up 64x
whoa what's going on x
there we go squared
and then if it was just like Plus
5X
plus 25
. now if I hit equals zero like they
have there I'm wondering if this is
going to do what I want it to do
is there a graph there
I don't see anything graphed maybe I'm
missing it
but as far as I zoom out I don't see
anything and so what I'm going to do is
I'm going to take away the equal zero
and notice that there's now a graph
there so sometimes if you type in the
problem from the SAT exactly into Desmos
for whatever reason it might not like it
and so my suggestion would be to either
take away the equal zero at the end
which is usually what causes that to
happen or
um well that's that's a good way to do
it and if that works then of course you
know go for that and now yeah we can see
that it's a it's a parabola it's kind of
hard to see it but it's still like a
U-shaped graph and you can see the
vertex there the minimum point at the
bottom 0 25
that was just an example I made up but
yeah that would be that problem and why
don't we use Desmos now in order to
solve maybe this question here the first
one here so it says in the X Y plane and
that's a good hint to use Desmos because
we're talking about a graph a line with
equation 2y equals c for some constant C
intersects a parabola at exactly one
point if the parabola has equation y
equals negative 2x squared plus nine x
what is the value of C so really quickly
we've got two equations they're
intersecting but we want them to
intersect in exactly one point and so
we're going to be able to figure out the
value of C such that these graphs
intersect like they said in just one
point so why don't we start by just
typing in I'll do the parabola first
that quadratic equation and it would be
y equals negative 2 x squared
plus 9x and another thing that I should
say is in Desmos if you want you can
pull open this keypad and I think on the
SAT that might be the default setting so
that you have this here and I could even
move myself so that you could see
some of the the functionality of this
you have numbers you have exponents you
have square roots things like that and
so you could always use that keypad
there instead of manually typing it out
on your own keyboard so that's helpful
too
so anyway let's go back to
this problem so we've got our first one
we see the parabola there I can go back
to the home default Zoom if I want and
then I'll type in the other equation
which is a line 2y equals c so 2y equals
c and uh-oh notice this little
exclamation point it's like an error and
this is an example of what Desmos
doesn't like so we typed in the equation
just as we saw it but for some reason
it's not really working and notice what
it says there it says we only support
implicit equations of X and Y so I take
that to mean there's no X in this
equation
so I need to add an X in you might say
well I can't just add an X in and that's
true but think about it there's not any
x's in it right now so we could actually
put in there C plus 0x
right because
there's no x's in the equation and so if
I put 0x in there 0 times x is just zero
it doesn't change anything right so
sometimes you're going to need to think
like that and put in plus 0x
but that's a rare problem or it doesn't
happen too often but that's what you
would do there so now notice that desmo
says that we can add a slider for C so
I'm going to tap that blue button on C
and look what it does
it gives you this slider and this is so
cool this is one of the coolest features
of Desmos you can move it yourself to
change the value of C to see what the
graph would look like if C was for
example 5 or 7 and you could see it
moving up and up and up now what are we
going to look for remember we want these
graphs to intersect at exactly one point
and so if I keep dragging this bigger
and bigger notice that that line is
getting closer to the top of the
parabola at the vertex there and it
seems like that's where it's going to be
able to intersect it in just one point
but notice that I've gotten as big as
though let me get for C and I'm not
there yet so what I'm going to do is I'm
going to tap on this number here 10 and
that's going to allow me to change the
range of c and clearly I need it to be
bigger than 10 so maybe I'll do
something like up to 25 I don't know I'm
just guessing and maybe the minimum I
can make it just 10 because I know it
has to be bigger than that so this means
C is between 10 and 25 five and I'm
going to assume it's probably going to
be a whole number answer sometimes it's
not but usually it is so I'm going to
put a step of one that means it's just
going to go up by 1 every time instead
of decimals like it was last time I was
sliding it and now I can hit enter and
you could see now that the slider is
going to go from 10 to 25 so let me drag
it and we're going to look for it to
intersect in just one point and uh oh
it doesn't seem like it's intersecting
it in just that one point notice that
it's a little bit off still
and so what I need to do is actually
seems like it's going to be between 20
and 21. so what I can do is I can go
back and I can change that step so that
it's not a whole number anymore maybe
it'll be like a half step so 0.5 and
maybe that'll help so 20 doesn't work 20
and a half also doesn't work but it
looks like our graph the vertex that
we're looking to to line up with is just
right between those two points right or
those two numbers so if I go down from a
half of a step to maybe a quarter point
25
that's probably going to work and so
there we have it 20.25 and you can see
that they intersect right there in that
one point and if I even zoom in more
drag this up you can see that it's
definitely just intersecting it in that
one point now there's of course other
ways you could do this without Desmos
but the point of this video and me
showing you this example is just to show
you that an example like this doesn't
need to be solved in Desmos but it
certainly could be and so you just need
to know what to look for when you're
using Desmos for these types of problems
so that first one we got it's 20.25 now
why don't we clear all these out you can
just hit these x's and it'll get every
get rid of everything and we'll go back
to the the home default zoom and why
don't we go over here and look for a new
problem that we can solve in Desmos so
we'll do this one next
64x squared we already kind of looked at
this one 64 x squared
plus BX
and you can see that it wants a slider
which is good equals zero now remember
the way I typed it in would that equal 0
before it didn't really seem to work and
you could see now that it's still not
graphing it so this is where again we're
going to take out the equal zero and now
it's okay it just needs that slider
which is great so let's go and add that
slider and it says in the question for
which of the following values of B will
the equation have more than one real
solution now in the context of a
quadratic like this a solution is an
x-intercept so if it has more than one
solution a real solution it just means
it's going to have two x-intercepts it's
going to cross this x-axis twice the
question is which B value does that now
you have two options you can take each
answer and plug it in in place of B so
you could just take out B here and put
negative 91.
and you could see what the graph does
now we actually got lucky here because
that first one we tried negative 91 we
don't even need this slider anymore
because look that graph does cross the
x-axis twice that would be more than one
real solution and therefore the answer
is just a negative 91. now if you didn't
plug in the answer like we did what you
could have done of course is like we
were going to do before put that slider
in and if you add the slider and change
it
um let me zoom out so that we could kind
of see the graph see it's way up there
if you drag it it's not really moving
much you might even not even be able to
really see it moving but that's because
these values for B that we need are big
numbers so I'm going to change the range
again and I need it to be
the smallest number is negative 91. so
why don't I put negative 91 and then the
biggest B value is 40 so I could type 40
and that would be the range of B and I
could put a step of 1 here and that
would allow us to to see what happens
and you could see clearly that when we
drag it to negative 91 it crosses the
x-axis two times like we already saw and
all the other numbers negative 80
that crosses it just one time
and positive five I mean you get the
idea this isn't going to work right it's
way up high it's off of our picture and
40 is as well okay so
either way we still get the same answer
it's a negative 91. hopefully you can
see just another good example of a good
way to use Desmos to get an answer very
very quickly if you did this problem
using algebraic methods without a
calculator it would just take you a
little bit longer unless you're really
really confident in using maybe the
quadratic formula the discriminant
things like that now why don't we just
take a look at maybe one more question
this is just another kind of similar
type of problem but it's another one
that we can use Desmos for so we'll get
rid of these and go back to the home
zoom and here's another example where it
says that they intersected exactly one
point so we're going to do essentially
what we did in the the one a little bit
ago I'll type in 2x squared and I don't
know if typing in the Y in front of it
is going to make a difference I think
it'll be fine so why don't I do y equals
2x squared minus 21x
plus 64. whoops what the heck
Plus
64. okay there it is graphed no trouble
with putting the Y there and then y
equals 3x plus a and here's our chance
to put a slider which is what we want
and we want these to intersect in just
one point but notice that that line has
a certain angle this time it's got a
slope of three so it's not just a
horizontal line like we saw in that last
example so this one might be a little
bit trickier to see but we know that the
a value
oh this one's actually different so
first of all we'll slide a so that that
line intersects the parabola just once
and you can see it's getting closer and
closer and it seems like negative eight
first of all it's a whole number so
that's a likely candidate for the answer
and of course now we can go up here and
we can see that if we zoom in and go
this way that these guys intersect in
yeah just one point which is right there
it looks like 6 10 okay so that is the
answer for where they intersect that's
good we're on the right track but do not
just pick negative eight and move on
because a is negative eight but they
don't ask for a they ask for the value
of x so be very very careful this means
that at the intersection point which is
what they say here they intersect at
this point x y that would be the point
that we just found here 610 and I can
just click that and it'll show me that
point so 610 and so the value of x at
that intersection point would be 6 and
our answer would be C okay so there's a
lot of different types of problems we
can use to use Desmos to find on the SAT
a lot of them have to do with quadratics
or systems of equations where we have
two lines or graphs intersecting I just
thought of one more that I want to show
really really quickly and I'm just going
to make it up off the top of my head to
show you that even a a simple problem
like solving equations can be used in
Desmos to find the answer so an example
might be if they gave you 4X minus and
let's try to make it really complicated
because
we want to see the power of what Desmos
can do x minus 7 equals let's say X Plus
9. okay so that might look pretty
complicated and certainly you can solve
it and I'm sure most of you know how to
solve that you would distribute the
negative two you would get all the X's
to one side get all the constants to the
other and solve for x but guess what I
put it in Desmos and I didn't even have
to think look this vertical line forget
about the fact that it's vertical the
line crosses the x-axis here at negative
five that means the answer for this
problem the value of x would just be
negative 5.
so easy so even on simple equation
problems like this if you don't want to
waste the time to solve it out and risk
making a mistake as long as you just
type it in correctly Desmos will show
you the answer because it's going to be
where that line crosses the x-axis so
um yeah we'll stop here there's plenty
of question types that you can use
Desmos for hopefully this was a good
summary of that and um yeah best of luck
to you when you're studying feel free to
check out our blog where we have good
resources on the SAT and on Desmos you
can check out our program methodize
which maybe you're already using right
now and you can also
take a lot of practice tests from the
sat's official website so good luck in
your studying and reach out to us if you
have any questions
hey thanks for watching let us know in
the comments if there's any topics that
you want to see a video on going forward
be sure to like And subscribe and check
out our channel for more content
5.0 / 5 (0 votes)