The only SAT Math DESMOS Guide you'll ever need

[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 another quadratic wait why is there a 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 right like it could have been 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 sponsor brilliant brilliant is a brilliant way to get better at the SAT Math see what that did there uh because their courses prioritize actual problem solving rather than memorization way too many students think that they can just memorize a bunch of formulas and then they're ready for the SAT but that's not how it works you need to a understand things conceptually and B solve a bunch of problems and this is brilliant's entire philosophy towards learning you learn Concepts through first principles with lessons that prioritize actual problem solving their measurement course in particular is a really great introduction to all the important geometry concepts you need for the SAT and unlike most test prep this is really well produced you have these nice Sleek animations I mean look at these I am I am physically attracted to these angles to get brilliant for free for a full 30 days you can go over to brilliant. org learnmath or or just click on the link in the pins comment below you'll also get 20% off a premium annual [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] 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 it's 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 minimum of f ofx + 5 is easy watch this [Music] that's right it grabs the translation for you this is crazy you can also do this for any other sort of Transformations so take advantage 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 doing is finding the 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 [Music] 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 you shouldn't I'm going to share my 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 Desmos some are worse 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.