Desmos Calculator Tips (ep 4): Digital SAT Strategy Guide

Summary

Mike Sattell, founder of Sattell Tutoring, presents a guide on utilizing the Desmos calculator for the digital SAT. He emphasizes the calculator's ease of use and its ability to visualize algebraic concepts, making complex problems simpler. The video covers graphing systems of equations, solving for x without an equation, and using sliders for guess and check strategies. Sattell encourages practice with the calculator to familiarize oneself with its features and to improve overall SAT scores.

Takeaways

• 📚 Mike Satter is the founder of Satell Tutoring and is providing strategies for the digital SAT in a 10-part video series.
• 🎥 The video focuses on effectively using the built-in Desmos calculator for the digital SAT, which eliminates the need to bring a separate calculator.
• 📈 Desmos calculator is primarily a graphing calculator that allows real-time visualization of equations and is free to use at desmos.com/calculator.
• 🚀 The Desmos calculator can greatly aid in solving complex math problems with ease and minimal practice.
• 🔍 The video demonstrates four specific ways to use the Desmos calculator: graphing and solving systems of equations, solving for x without an equation, visualizing changes to equations, and using SAT strategies like guess and check.
• 🤔 The Desmos calculator is considered superior to traditional graphing calculators due to its intuitive interface and fewer buttons.
• 📊 By using the Desmos calculator, students can avoid common mistakes and save time on the SAT, especially for system of equations and algebraic problem-solving.
• 💡 The video emphasizes the importance of practice with the Desmos calculator to become familiar with its functions and shortcuts.
• 🎯 The Desmos calculator helps visualize algebra, making abstract concepts more concrete and easier to understand.
• 📈 The video encourages students to use the calculator as much as possible during the SAT to maximize efficiency and minimize errors.

Q & A

What is the main topic of Mike Satell's fourth video in his 10-part series?

The main topic of the video is how to effectively use the built-in Desmos calculator for the digital SAT.

Why does Mike Satell recommend subscribing to his channel for those planning to take the SAT?

He recommends subscribing because viewers can access all the videos and resources he has released, which are interrelated and provide a comprehensive understanding of strategies for improving the overall SAT score.

What is unique about the Desmos calculator according to Mike Satell?

The Desmos calculator is unique because it is a graphing calculator that is built into the digital SAT app, it's free, and has an intuitive interface with fewer buttons, making it easier to use than traditional graphing calculators.

How does Mike Satell suggest using the Desmos calculator for systems of equations?

He suggests entering the equations into the calculator, which will then graph them and automatically calculate the points of intersection, including X and Y intercepts, allowing for quick solutions without the need for algebraic manipulation.

What is a common trap that test-takers might fall into when solving systems of equations using the Desmos calculator?

A common trap is mistaking the coordinates of the points of intersection, such as confusing a positive number with a negative one, leading to the selection of incorrect answer choices.

How does the Desmos calculator handle equations with no Y coordinate or variable?

The Desmos calculator can graph equations with no Y coordinate or variable by displaying vertical lines at the X values derived from the equation, allowing users to identify valid answers like -5 or 3 as shown in the example.

What strategy does Mike Satell advise for dealing with complex equations involving square roots?

He advises entering the equation as written into the calculator, utilizing the keyboard function to input square roots and other complex elements, and then letting the calculator solve and graph the equation to identify the correct answers.

How can the Desmos calculator assist in visualizing changes to equations and graphs?

The Desmos calculator can visualize changes by allowing users to manipulate functions and equations directly on the graph, such as adding or subtracting terms, and observing the immediate impact on the graph's shape and position.

What is the advantage of using the Desmos calculator for guess and check strategies?

The advantage is that the calculator enables quick testing of different values and immediate visual confirmation of the results, reducing the time and effort required compared to manual guess and check methods.

What does Mike Satell emphasize as the most important aspect of using a graphing calculator for the SAT?

He emphasizes that the most important aspect is the ability to visualize algebra, as it allows test-takers to see the shapes and movements of equations and understand complex concepts more intuitively.

What advice does Mike Satell give for test-takers on when to use the Desmos calculator during the SAT?

He advises test-takers to practice with the calculator to know when to use it and when to rely on pencil and paper methods, and to use it as much as possible to minimize errors and maximize efficiency.

Outlines

00:00

📚 Introduction to Desmos Calculator for SAT

In this introductory segment, Mike Satell, the founder of Satell Tutoring, begins the fourth video of his 10-part series focused on strategies for the digital SAT. He emphasizes the Desmos calculator, a built-in tool for the SAT app, and encourages viewers to subscribe to his channel for comprehensive resources. Mike highlights the Desmos calculator's basic features and how they can significantly impact one's SAT score with minimal practice. He also mentions that while other tutors have created programs detailing the calculator's functions, his video will focus on the highlights and quick strategies for using the calculator effectively.

05:01

📈 Graphing and Solving Systems of Equations

Mike demonstrates how to quickly graph and solve systems of equations using the Desmos calculator. He advises against wasting time on algebraic solutions and instead shows how the calculator can efficiently identify points of intersection. Mike warns viewers to avoid common traps set by the SAT, such as confusing x and y coordinates, and emphasizes the importance of double-checking work. He also discusses the benefits of using the calculator over traditional algebraic methods, noting that it reduces the chance of making careless mistakes and saves time.

10:03

🔢 Dealing with Equations without Y Coordinates

In this part, Mike addresses a unique situation where an equation lacks a Y coordinate or variable. He explains how to input such equations into the Desmos calculator and how it handles square roots and other complex elements. Mike points out that while the calculator doesn't graph these equations as traditional curves, it still provides the correct x values, represented as vertical lines. He stresses the importance of practice to familiarize oneself with the calculator's functions and argues that the calculator's algebra-solving capabilities can save significant time and reduce errors.

15:03

📉 Adapting to Changes in Equations and Visualizing Algebra

Mike discusses how to adapt to changes in equations, specifically focusing on a scenario where an f(x) equation is altered to form a new G(x) equation. He illustrates how the Desmos calculator can visually show the shift in the graph of the equation, helping to identify the minimum value of G(x). Mike emphasizes the calculator's ability to visualize algebraic concepts, which can be particularly helpful for those who struggle with abstract algebraic thinking. He also touches on the SAT's tendency to create situations where mistakes are likely, advocating for the calculator's use to minimize errors and verify instincts.

🎓 Conclusion: Maximizing the Desmos Calculator's Potential

In the concluding segment, Mike reviews the key points discussed in the video, reiterating the Desmos calculator's usefulness in graphing systems of equations, solving complex algebra, and visualizing changes in equations. He stresses the importance of practicing with the calculator to become comfortable with its functions and shortcuts. Mike also acknowledges that while the calculator is a powerful tool, it won't solve every SAT question and that some problems will require manual solutions. He encourages viewers to continue exploring the calculator's features and to seek out additional resources to enhance their SAT preparation.

Keywords

💡Desmos calculator

The Desmos calculator is a built-in tool within the digital SAT app that students can use to graph equations and solve complex problems without needing to physically bring a calculator to the test. It is a graphing calculator that allows for visual representation of mathematical concepts, making it easier for students to understand and solve problems. In the video, Mike Sattler emphasizes the importance of practicing with the Desmos calculator to familiarize oneself with its interface and capabilities to improve overall SAT scores.

💡Digital SAT

The Digital SAT refers to the transition of the traditional paper-based SAT (Scholastic Assessment Test) to a digital format. This change allows students to take the standardized test on a computer, which includes the built-in Desmos calculator for mathematical problem-solving. The video series by Mike Sattler focuses on strategies specifically tailored for the digital SAT, aiming to help students adapt to this new format and maximize their performance.

💡Graphing

Graphing is the process of visually representing mathematical equations or functions on a coordinate plane. It is a fundamental concept in algebra and is used to understand the relationship between variables. In the context of the video, graphing is a key feature of the Desmos calculator that allows students to visualize equations and solve problems by observing the graphical representation of the equations.

💡Algebra

Algebra is a branch of mathematics that uses symbols and rules to solve equations and understand the relationships between quantities. In the video, algebraic concepts are central to the strategies discussed for the digital SAT, particularly in using the Desmos calculator to simplify complex algebraic problems and visualize solutions.

💡Subscription

A subscription, in the context of the video, refers to following Mike Sattler's YouTube channel to gain access to all parts of his 10-part series on strategies for the digital SAT. By subscribing, students can receive updates and access to the full range of resources designed to help them improve their SAT scores.

💡Practice

Practice, as emphasized in the video, is the act of repeatedly applying oneself to a task or skill to improve performance and mastery. Mike Sattler stresses the importance of practicing with the Desmos calculator to become familiar with its functions and to enhance problem-solving abilities for the digital SAT.

💡Strategy

A strategy in the context of the video refers to a specific approach or method designed to solve problems or achieve a goal, particularly in relation to test-taking for the digital SAT. Mike Sattler's video series aims to provide students with various strategies to tackle different sections of the SAT more effectively.

💡Visualization

Visualization in mathematics is the use of graphical or pictorial representations to understand and solve problems. In the video, Mike Sattler highlights the Desmos calculator's ability to visualize complex algebraic equations, making them more accessible and easier to comprehend for students.

💡Guess and check

Guess and check is a problem-solving technique that involves making an educated guess and then checking to see if it leads to the correct solution. In the video, Mike Sattler discusses using the Desmos calculator to employ this method by testing different values and observing the graphical outcomes to find the correct answers.

💡Trap answers

Trap answers are decoy options in multiple-choice questions that are designed to catch out test-takers who may not fully understand the problem or who may make careless mistakes. In the video, Mike Sattler warns students about the SAT's tendency to include trap answers and emphasizes the importance of using the Desmos calculator to avoid falling into these traps.

Highlights

Desmos calculator is built into the digital SAT app, eliminating the need to bring a separate calculator.

Desmos calculator is primarily a graphing calculator, allowing real-time visualization of equations.

The Desmos calculator is free and can be practiced with at desmos.com/calculator.

The calculator simplifies solving systems of equations by graphing and finding intersection points.

Desmos calculator automatically calculates X and Y intercepts for graphed equations.

It's important to avoid trap answers and double-check coordinates when using the calculator.

The calculator can handle equations with square roots, simplifying complex algebraic problems.

Desmos calculator allows for visualizing changes to equations and graphs, enhancing understanding.

Using the calculator can help apply SAT strategies like guess and check in a more intuitive way.

Desmos calculator is more intuitive and easier to use than traditional graphing calculators.

Practicing with the calculator at home helps familiarize users with its functions and shortcuts.

The calculator can solve for X even without a complete equation, by graphing and identifying valid answers.

Desmos calculator can be used to adjust and compare graphs, aiding in finding the minimum value of a function.

The slider feature on the calculator allows for easy guess and check of values in an equation.

The visual aspect of the Desmos calculator helps conceptualize abstract algebraic ideas more concretely.

By using the calculator strategically, students can save time and reduce the chance of making careless mistakes.

The Desmos calculator can handle a wide range of mathematical problems, making it a valuable tool for the SAT.

Transcripts

hey everybody I'm Mike satell the

founder of satell tutoring and this is

the fourth video in my 10 part series

covering all of the strategies for the

digital SAT but this video can be

watched in isolation I think in fact a

lot of you might come to this through

other means so you don't need to watch

all the others I'm just going to hit the

highlights for how to use the built-in

Desmos calculator but I do recommend

that you subscribe to my channel because

then you can see all the other videos

all the resources that I've released

they are all much more interrelated

working through different strategies and

kind of referencing other videos so if

you are a subscriber then you will get

to see the entire big picture which is

the best way to improve your overall

score I'll also include a few of the

more comprehensive analyzes of the

calculator strategy for the digital sat

in the description of my video some

other tutors have made some really great

programs that go through all the

different little things that the

calculator does but I wanted to as

quickly as possible give you the

highlights the stuff that can change

your strategy and your score with very

little practice and very little

understanding of how the calculator

works just using its basic features so

hopefully this will make a big change in

just a couple of minutes let me just

talk quickly about what with the Desmos

calculator even is it is built in to the

app that you will take the digital sat

on so you do not even need to bring a

calculator with you to the SAT anymore

now I still think you should something

simple something like a scientific

calculator just like this one it has you

know basic functions it does have some

more advanced stuff but I would only

really use it to do some crazy

multiplication or division or addition

like the more basic stuff let the Desmos

calculator be where all the fun stuff

happens and that's because the Desmos

calculator is a graphing calculator

mostly so we can see all these equations

in real time

and the best part about it is it's free

and you can use it right now if you want

by going to desmos.com calculator I

definitely recommend that you're

planning to take the SAT you use this

calculator in your practice so you can

get used to how it feels and what it

does and where all the buttons are it's

definitely a little complicated at first

but with practice it should be second

nature how to work through some very

complicated math and make it much much

easier in this video I'm going to show

you four specific things okay I'm going

to show you how quickly we can graph and

solve systems of equations how we can

solve for x even if we don't have an

equation per se and I can show you how

we visualize changes to equations and

just graphs in general and how we can

use sat strategies like guess and check

even on this calculator so it does

really lend itself to the sat in

particular because it lets us play with

some things and test out answers in ways

that a normal graphing calculator might

not be able to do and that's the thing I

think that the Desmos calculator is

better than any real life calculator

graphing calculator they've ever seen it

just has fewer buttons things are more

intuitive it's easier to use so

hopefully you feel the same way let's

Dive Right into a first question here

this is pretty straightforward system of

equations you got two equations here and

in math class and school you would be

asked to solve this system probably

algebraically by either doing some sort

of substitution or elimination something

where we would eventually end up with an

x equals or a y equals but I wouldn't

bother with any of that here don't waste

your time the calculator at its best is

just going to let you see where the

point of intersections are so you can

see here I've already taken the time to

just enter the two equations make sure

that they're correct that you don't

accidentally enter the wrong numbers but

otherwise just enter them in and if you

look at the red line here you can see

that it's also automatically calculating

your X and y-intercepts that's very

convenient for other questions but the

blue line is off the screen so we should

scroll around until we find a point of

intersection and again if you click it

you'll see it just pops up it does the

calculating for you negative 9 negative

44. so what's happening here though is

they're trying to get you into a trap

with Choice C so we should zoom out or

we can hit the home button to go back to

the origin and now find another point of

intersection that actually gives us an

answer choice and if we zoom out we can

see there's the one that we had before

negative 9 negative 44 and now 14 is the

correct answer because that is the x

coordinate of the other point of

intersection

so what do we have to do to solve this

question basically just type some stuff

into a calculator and scroll around and

boom the calculator just gives you the

answer of course there are going to

still be some trap answers maybe we

misread a number we confuse that 9 and

negative 9 are different numbers and so

we pick C or sometimes what they'll do

is they'll ask you to solve for x but

then they'll give the y coordinate of

the point of intersection just to

confuse you so always double check those

things but otherwise there's really no

way to make some careless mistakes here

whereas if I did solve this with algebra

it would be long it would be tedious and

the chance of me just calculating

something wrong moving an X in the wrong

place it's very very high and so I could

waste a lot of time just to get the

wrong answer this is so much better

pretty much every system of equations

you're now going to want to enter into

the calculator some of you who are

really great at algebra might find some

situations where it's better to do it by

hand to use your scrap paper and and

show the work but you know with practice

you'll you'll figure out those

situations and for some of you if you

don't have that sense of whether it's

going to be easier to do by hand or

easier doing the calculator then just

always do it in the calculator it

doesn't matter it's still going to be

effective and efficient if you enter

these things quickly

let's look at a slightly weirder

situation uh here's another equation but

this time it's just one equation notice

there's no Y coordinates no y variables

here so

um there are a couple of ways to handle

this uh definitely though if I were

looking at it I'd be like I don't really

want to solve this algebraically by hand

because it's got square roots it just it

seems risky and what we should do then

is enter it as written into the

calculator so if you're having trouble

with square roots you can hit the button

on the bottom the little keyboard button

and it'll bring up all the functions so

you can hit that and then you can type

the rest so 3x minus 10x equals

or you can also type the letters sqrt

and it'll Auto generate the square root

symbol for you so this is why you should

practice at home get used to that stuff

um when we graph it you'll see that we

get these two vertical lines and if we

zoom out they're just kind of straight

lines up and down the whole way so

there's nothing fancy it's on a curve

like the other ones before but they

happen at negative five and at three

and basically that's just giving us the

answer either negative five or three

would be valid answers to this question

you don't need to Bubble both right

notice the question just says what is

one possible value so just pick one but

both are acceptable

so let me just explain what's happening

here because there's no y equals this

calculator is not graphing this like we

would think of like a regular line or a

parabola or anything that kind of Curves

around it it doesn't have the kind of

shape that a normal equation with a Y

and an X would have

but what the calculator is kind of doing

here is just solving the algebra for us

so it's it's kind of ending in the same

place that you would end if you did this

by hand right you'd have x equals

negative 5 and x equals three as your

two answers and you box them and you'd

be like hey I did it so what that looks

like though is a vertical line at

negative five is the x equals negative 5

equation and to draw x equals three on a

graph you would get a vertical line at x

equals three so it's kind of just giving

you the X values but they're gonna look

like these vertical lines but that's

okay as long as you're comfortable with

that you you've just let the computer do

all this solving for you that's awesome

that's what we want

um the the reason I would definitely do

that here is the square roots

the square roots maybe are also causing

a little bit of a problem that I noticed

sometimes with this strategy which is we

can't click the x-intercept and and get

the actual point like we could before

when you're doing the intersections or

the intercepts there so I think that the

reason that happens is the square root

is just like a messy thing and the the

computer can't really like give us that

point but it doesn't matter right we

could zoom in we can kind of clearly see

that the the lines go through negative

five and three I guess it's possible

that instead of going through three it

goes through like

2.99999999 forever but like the odds of

that happening are very slim and and we

can of course keep zooming in and really

just make sure that the vertical line is

where it looks to us and that saves us a

huge amount of time and headache and

chance of a mistake by actually being

able to just let the the machine the

calculator do the calculating for us so

not only is it a graph but it also is an

algebra solver this is really really

helpful and just like before there might

be cases there probably will be cases in

fact we're letting the calculator do the

algebra is a waste of time the algebra

is so easy or something that it's just

better to just do it yourself

but again if you are not good at

determining those situations then you're

probably just not good at algebra and so

you probably do want to default to the

calculator as much as possible to just

do as much of the work as possible for

you because you cannot be trusted to do

it yourself without errors but this is

why you practice the the test the same

way you would take the test have the

calculator ready to go and know when try

to figure out when you should go to it

and when you should do things with a

pencil pencil and paper your scrap

um let's take a look at another one

here we have a a question that would

definitely throw people off it's giving

us an f of x equation that's kind of

complicated it's also then telling us to

change that equation in some way by

talking about a new equation G of X that

has this f of x minus four piece

um and then we have to find the minimum

value of both of these or I guess I'm

the G of X equation so what would throw

people up here is they don't understand

like intuitively how the graph is going

to move some of you might

but I do find that this is also one of

those cases where people are prone to

error so I wouldn't trust just my logic

and my knowledge I'd want the calculator

to show me that my instincts are correct

so what we can do is not only use y

equals to set up an equation but we can

use function notation itself so we have

f of x here setting us up so that way we

can type the original f of x equation

and then the second line I typed the G

of X equation using f of x and so it's

literally just the two things that they

gave us in the question I just type them

as is and let's see it's going to show

us what happens as we change this so you

can see oh here yes the letters are all

given so if you can if you have a

keyboard for some reason you can always

find the letters in the keyboard thing

and we get a parabola and there's our

vertex negative 12 4 and you can see

there's a trap because that's the

original minimum but if we turn on the G

of X we see that it shifts to negative

eight which is the correct answer and we

can turn off the one we don't want so

we're not confused and and that's really

it is is we're able to see this graph

move in a direction rather than have to

actually just like guess it what the

direction is going to be or think about

it we can see it and know for sure so

there are definitely ways to do this

manually to find the vertex of a

parabola manually to shift a graph

manually

but why why do it why even open the door

to a possible careless mistake just let

the computer solve it for you let the

calculator Desmos do the work and and

that's really kind of like the whole

point of this is that you have to

recognize the SAT is very good at

creating situations where you're going

to make a mistake it's good at forcing

errors

so knowing that we have to be humble and

doubt ourselves and be able to just know

when to to put it into the calculator

instead and let that thing do the work

let's look at one more situation where I

think it would be difficult uh with any

other graphing calculator to kind of

solve in a in a good way so here's a

question where we don't have an equation

actually we have an expression so

there's no equal sign but you can see I

set up the first equation the first

expression as an equation by just

throwing in a y equals and basically

what that lets me do is is see this

thing more like the kinds of grass I'm

used to right where it kind of moves

along the x-axis and goes up and goes

down and all that stuff so I'll zoom in

in a second but you can kind of see it's

got like a little bump at the origin

now they're asking us to figure out what

the an equivalent expression would be so

uh we can definitely just take this

second equation and type it into the

second line and again I'm going to use a

y equals to do that

and we can see the keyboard will let us

do all of this if we don't want to type

or we don't have a keyboard so y equals

and I'm going to type the 3 and then

obviously create a fraction is just

division so just use the division symbol

and then x squared plus K and you'll see

when I hit the k

it's in the letters and we get this

option to add a slider so we're going to

click that and we can see a new line

comes up and it literally is a slider if

you slide it you see all the different

versions of this equation as if K is

different numbers but we don't want it

to be random numbers let's try the

numbers that are in the choices so we do

seven and we zoom in we can see these

these two expressions are very similar

but look they're not quite the same

there's a little difference so if we

change it to eight though we can see now

the two green and black lines overlap

and we can turn them on and off and see

that it's literally the same thing if we

try the other choices we can see again

21 they're different 392 it's going to

be different and so we know now that 8

is the answer because we were told to

find an equivalent expression and by

playing with this value of K with a

different guess and check answer choices

that we have we can see which one gives

us the graph that's the same so normally

you know old SAT no calculator we would

have to do this by hand and think about

this conceptually and algebraically and

understand why the equations are

actually the same but with the graphing

calculator we can just see what's going

on much more easily we can test these

different numbers out even if we don't

know it for sure the slider lets us plug

things in we can either use the slider

that's there or you saw me typing the

specific numbers that I wanted and as I

change them the graph of the equation

changed as well and we can just wait

until we get the equation that we want

because the graph will be what we want

it to be and so these equivalent

expressions should produce equivalent

graphs and they only did it eight I

could see it there was no doubt in my

mind in fact I still don't really know

why that's the case I don't care I have

the answer and so very quickly within

just a few seconds this very hard

question becomes much easier and you can

get it confidently and there will there

will be plenty of questions where you

can't use the calculator this way but

now you have more time to do the hand

and scrap paper kind of stuff that you

need for those other situations it's

really the calculator is a great tool it

is not going to solve every single

question on the SAT but if you can use

it more often to claw back some time

then for the truly difficult stuff you

will be able to kind of hopefully finish

just by doing it by hand

let's review what we talked about here

again the calculator is built into the

section you don't need to bring a

calculator but you can if you want just

have a backup but you should get

comfortable with the Desmos calculator

as you practice get used to where the

buttons are get used to how to type

things get used to all the little

shortcuts and like I said there are

other tutors out there with videos that

are much longer that are going to go

into much more detail about what this

calculator can do there are some other

features I'm skeptical of some of them

as as being more efficient but maybe for

you you'll like them so go into that

other tutors and check out what they're

doing but for me the the key pieces are

what we talked about it lets us graph

systems of equations very easily it lets

us solve for x for very difficult

algebra very easily and we can kind of

use this slider to play around and even

if we don't have a specific value we

have to kind of find a value we can

guess and check our way to it and the

the third bullet point there is I think

the most important one in in all of

these cases the thing that a graphing

calculator lets us do is visualize

algebra what so many people struggle

with in algebra is it's all kind of

conceptual and Abstract right what is

this x it's a number but it's not a

number it's a number we don't know and

so it's difficult to wrap your brain

around what's even happening but with

this uh graphing calculator we can see

what an equation looks like it creates a

shape right we could compare shapes we

can see shapes change and move and where

the shapes cross these are all really

powerful things that I think tap into

the way the human brain really works so

we're going to use the calculator to

just think the way our brain wants us to

think it's it's just a really great

addition to the test I think it's going

to make some of the math way easier for

a lot of you so we want to be able to

take advantage of it and I hope this

helped again there's more out there so

feel free to keep uh commenting on any

other new features that you really like

that I didn't get to in my my lesson

here but please subscribe go check out

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especially we might not be able to use a

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strategies so please subscribe it really

helps me out and remember when it comes

to your scores don't settle for less so

tell for more thanks for watching