20 SAT Math Questions You Can Annihilate Using DESMOS

what's up everybody good to see you we are going to spend a little bit of time together I'm going to show you 20 questions that you absolutely must know how to do using Desmos they are of varying difficulty so a few might seem a little easy for you some will seem kind of on the intermediate side and I guarantee you there will be a few where you are really going to learn a lot they'll be very hard those would be the questions which you otherwise would never have been able to do without Desmos or if you attempted to do it without Desmos it would take a really long time um let's see guys three quick things and then we're going to jump right into this first question first um please don't be passive uh when you watch the video please make sure that you have Desmos live and ready to go and follow along with me okay that will develop good muscle memory so that when it comes to the test uh coming up by the way on March 9 and any future edition of the digital sat that you might take you know exactly how to approach the question you're not going to hesitate and you can just crush it using Desmos um second please get a mouse okay I strongly believe that it will enable you to zoom in and out real fast as you can see that I'm doing right here as well as pan around because it'll help you get certain features of your graph much faster um and just make sure that it has a wheel and that allows you to um move around extremely quickly okay and the final thing is just understand that Desmos is super powerful we think of it for the cing capabilities but it also does basic calculations so it's fine to bring your physical calculator uh most students use the ti84 plus C that's totally fine but I would not use it for basic calculations use Desmos so if you had to do 54 * 5 bam there's your answer why would you waste time going to the calculator and then back to your computer right so the only situation where you should use your physical calculator is if you have some handy formulas stored in it okay also remember that the SAT does provide a little reference sheet um and I just clicked on it and as you can see you get some fairly handy geometry formulas okay uh we're ready to get started here guys I'm super excited uh let's attack number eight here this is by the way from a blue book emulator that um I use for my students these questions are exactly like what you're going to see on the SAT so we have x = 70x + 3 and we need to get the negative solution always remember to um focus on little details in the question guys so that you don't make accidental mistakes cuz there may be more than one solution we need to make sure it's negative so all we're going to do is just literally type the equation directly into Desmos it will solve equations for you automatically so X is 70 over um x + 3 and if it seems like I'm typing a little slow and I'm having to look down and hunt for things it's just because my microphone is directly in front of me so do excuse me if it seems like like I'm uh kind of like uh uh bumbling about there so X is 70 overx + 3 pretty cool now we have two vertical bars two vertical lines those do not represent the graph of the equation they represent the solutions and you get them by just uh going directly to where they hit the x-axis and this is the one that we want we would ignore the other uh because it's positive obviously and here we go and we just zoom in and you just zoom in enough where you're convinced that you know the answer it would be -10 in this case right guys so 10 it is and what do we do we just type in -10 and there you go um and then just hit next and that will commit the answer for you okay guys here is our next victim um number 10 and uh this question says given the function uh yal F ofx graphed in the XY plane what is the Y intercept okay so again focus on that we want the Y intercept not the X and I think the easiest thing to do here would be to Simply copy that function Direct ly into Desmos incidentally you will not be able to on the actual test um sadly you will not be able to copy anything from the problem and just you know paste it directly into Desmos so we will just rewrite this F ofx uh equals 27 time 2/3 and then we're going to raise it to the X power um let me just get rid of that parenthesis now to raise something to a poweru you need to just go shift six okay shift six and then bam there's your exponent now what do we do next um we want to see where this graph hits the y- axis so we just uh pan up a little bit and uh Desmos is smart so if you see kind of like a little gray Dot and then it turns black that essentially means that it knows where the uh intercept is and there is your answer 0 comma 27 and we're going to pick C uh make sure that your answer lights up blue then hit next and that commits your answer all right guys next problem number 12 uh incidentally these questions right now that I'm doing are on module one so those do tend to be maybe on the slightly easier side um it says a triangle has a height of X cm and a base length of x - 3 cm if the triangle has an area of 104 sare CM what is the value of x so you will get scrap paper on the test and it'll be completely fine in fact I would encourage it to maybe just sort of write the information down and set up an equation my point however is once once you set up that equation do not do any more work by hand feed it into Desmos okay so the way it would work is as follows uh we know that the formula for an area of a triangle is area equals 1/2 base time height again you could just confirm that on your reference sheet you see it right over here okay so what we're going to do is we're just going to say the area is 104 I don't need to solve for the variable okay decimals will do that for you so the area is equal to and now I'm going to uh set up the formula so it's 1/2 so 1/2 the way I got that fraction by the way is you just use the little fraction bar it should be directly next to the shift key on your keyboard now next what is the Bas has a Bas base length of xus 3 so I'm just going to write x - 3 in parenthesis and it has a height of X and so I'm just going to include the X like that and guess what guys we're done can you believe it we're done you might think yeah but where is the graph uh just hit the home button um because then that'll get you closer to where the action might be and now we're just going to zoom out a little bit and Bam look at that again two vertical lines that represents the two solutions obviously we want to pick the positive one uh since it's a length and lengths are always positive we're going to zoom in a little bit and I think you guys would agree that the answer is going to be 16 uh this is multiple choice though that means you have a lot more forgiveness and you don't have to worry about getting exactly precise um on locating Your solution uh even though it's pretty obvious it's going to be 16 comma 0 so we're going to click B 16 and we're going to move on all right guys get ready this one I think is like the first point in the test where you're going to be like oh everything's been going great and like oh no even in module one they're throwing you know a a fairly hard question at me uh you I think you guys are going to be blown away how easy this is uh Desmos essentially hands you the answer uh let's just read it first it says ailia Made a deposit in a savings account at a bank and then made no additional deposits or withdrawals the table shows the exponential relationship between the time Y in years since a milus deposit and the total amount D in dollars in the account which equation best represents the relationship between Y and D okay now what you're going to do okay is you're going to notice that they told you that the E that the relationship is exponential we're going to create a table that basically just copies those values directly into the table and then guess what guys we're going to uh basically get the equation equ of that exponential relationship and I'll show you exactly how we do it so let's just get rid of this and now to get a table the fastest way to do it I'm going to teach you a few shortcuts as we go just simply type the word table okay next we're going to enter the data um you're going to have zero 1 and two for the X values and then we're going to enter the Y values which were uh 740 um 74370 and 74742 and again forgive me I know I'm looking all over the place it's just because I've got this big microphone right in my face so we've got 740 740 370 740 742 perfect okay and now what are we going to do next guess what we are going to use Desmos his awesome little equation um I would call it like uh the the equation um Creator okay so all you have to do is notice that uh the table was set up up as x sub one and Y sub one so you do need to type those exactly as is so we're going to go y sub one to get a subscript you go shift and then the um minus sign which is you know on the upper layer of your keyboard notice it went down into subscript type a one and then to get out of that subscript use the right arrow okay now this is extremely important this symbol is basically what hands you the equation that it's going to give you you have to go shift and then the little uh button directly next to the number one directly to the left of the number one that looks like a little tild day symbol that you might see in Spanish class on top of the NS and now we're ready to nail this thing so we're saying that we want to get an equation where y sub 1 is going to be expressed as an exponential equation the general form is simply a * B to the X so that you should know um and so you would go a and then B and now we want to raise that to the power of so that's shift 6 and then I'm going to type x sub one sub means subscript so remember that's shift and then the minus sign and now look at that little one that I get there and I'm going to scroll down a little bit and guess what do you see what it gave me under parameters it gave me the values for A and B which means that my equation is y equal a which is 740 * 1.05 to the X power and that's it um you wouldn't really even need to graph it at this point that wouldn't necessarily achieve anything but maybe I will do that just for the fun of it just so that you guys see that it did create a beautiful exponential equation so 740 * 1.05 and we're going to raise that to the X power okay and just zoom out a little bit and there it is okay so this is essentially what we got and if you look in if we zoom in a little bit these are the three points and basically what Desmos did is it took the three points from the table and it form fitted the exact exponential equation to go through those three points how cool is that and so I think it should be pretty obvious that the answer is going to be uh what is the answer going to be it's going to be C right because that's the one that says 740 * 1 .005 the same as 1 plus .005 uh to the X power uh notice that um that in this particular case I'm not worrying about the variables that they gave um just use X1 and y1 okay and there you go so let's now move on to the next problem okay guys we are now on number 14 uh we have y = 7x and Y = X + 18 at how many points do the graphs intersect in the XY plane so notice it's saying at how many so we basically just need to count how many times these two equations May intersect one another I'm going to give you a quick little shortcut when you've got multiple things going on and you're ready to start a new problem you don't have to keep hitting the x button just hit the little gear icon hit delete all and Bam you're at the top okay so we're going to enter y = 7x and the next equation is y equals x + 18 and we're going to just see where these guys intersect and because they're two lines it should be pretty obvious right that they can only intersect at that one point okay we don't really care what the value is but just so you're in case you're curious you would click on that that would immediately get you the value of their intersection point which is at 3 comma 21 but the point is they only intersect once and so we pick B one and we're done with that question okay guys moving on to our next problem so now we are going to get the actual intersection point so this question says 9x + 6 Y is 30 4x + 3 Y is 18 and we have to get the value of x again I can't emphasize enough guys um you know you are able to crush these questions in a matter of seconds so don't waste that opportunity by picking the value of y for example okay so make it super clear what your goal of the question is and make sure you pick the um corresponding answer so we want to make sure we pick the x value not the Y value okay let's get rid of these two guys let's type these two equations in 9x uh plus 6 y again bear with me silly microphone right in my face and then we have 4x + 3 y uh equals 18 okay not 19 but 18 okay and notice that there's this cute little uh gray dot that appears and then when it turns black that pretty much guarantees that that's the correct uh intersection Point um yeah that gray dot right there and I just turn it black and then if I zoom in uh you can be you can be rest assured that that's the intersection Point okay so what's the answer we want X it's -6 notice that guys that they did put 14 in there for those students who are just a little bit too fast and are not trying to uh read carefully what the question's asking for so of course we're going to pick uh a -6 that will be the answer and we're going to move on to the next problem all right guys we're getting close to the end of the module so you should anticipate the questions are going to gradually get a little bit harder and um let's see what we can do with this one it says the function f is defined by f ofx is 12x^2 - 30X - 162 for what value of x does it reach its minimum value this is an automatic don't even think about it just immediately enter that equation that function directly into Desmos and you're simply going to click on the vertex because the vertex always corresponds to either the minimum or the maximum value so here we go this is an absolute dead giveaway type question uh you you have to make sure you absolutely get it correct okay - 30X - 162 and we are going to uh hit the home button because it might just allow us to see what's going on a little bit better and we just zoom down see I can do this so fast with the mouse and here we go we want to get in a little close just so we're certain that we got the correct value and notice that gray dot turns black there's the uh vertex so the coordinates are 1.25 that would be the x value and the y coordinate is 0.75 once again guys let's not drop the ball it says for what value of x does it reach its minimum so what am I going to put the 1.25 right we're going to enter 1.25 and we are going to collect um all the points that we deserve for that question okay guys so now we are getting close to the final boss we are at number 21 remember each of your math modules will have exactly 22 questions so here we go uh in the XY plane line M passes through the point 0 0 and is parallel to the line represented by the equation Y = 7x + 5 if line M also passes to the point 4 comma n what's the value of n so there's a lot going on on here it might be kind of hard to kind of like figure out exactly how to approach it I think the cool thing about Desmos is that you can visualize what's going on and then you might be able to come up with a really clever idea to kind of like fast forward through the problem and I'll show you exactly what I mean here so the first thing we can do is just without even thinking you have to enter that equation so y = 7x + 5 because we have to make sure that the other one um is going to be parallel to it so here's 7x + 5 okay perfect now the next thing I want to do is line M is going to pass through the point 0 0 so guess what Desmos of course allows you to enter points so we're going to enter the point 0 0 however what I'd like to do is include the other point directly next to it and the cool thing is I'm going to connect them with a line it'll be much easier to visualize another line parallel to that line rather than to just use two points so you can do more than one point on the same line in your Desmos entry bar and we're going to go comma and now we're going to enter the other point 4 comma n and of course the N will pop up as a slider and we definitely want to use that slider so we'll click on n and now we've got a cool little slider um but you would agree right it's not terribly useful right now because it's going to be kind of hard to figure out how that point would be parallel to the uh to the line okay so what am I going to do click on the little icon in blue with the little dots hold it down okay don't just click and then release hold it down and then do you see the option at the bottom with lines just move that to the right so it's toggled on and look at that guys you now have a line that connects the two dots which is going to make our task much easier to figure out how this thing is going to be parallel now notice that as I increase my value of n right it is starting to get slightly more parallel to the red line but not yet so let's actually adjust and to maybe go from 10 cuz we already know that 10 didn't work so let's now use that as a lower boundary notice that you have total control over the range of your values for your slider as well as the step size in case you want a little bit more Precision so I'm going to make it go from 10 to say 30 okay um we can still keep the step size as one that's fine and now let's see what happens as I move this ah look at that it's getting closer and closer and it looks to me like we're starting to laser in on this um we might want to zoom out because that might help tell me if it's parallel or not and notice that we are starting to get pretty darn close aren't we now I will admit myself that it's a little hard to tell the difference right now between say 27 and 28 right and unfortunately because this is a Student Response question we have to be you know we have to be exact okay if we put in 27 and the answer was 28 it would be wrong with multiple choice you have much more forgiveness and you probably would already get the closest answer um so we have to be careful here and because it's only two points um we don't get to see the full extent of the line so basically what you could do is say to yourself wait a second I know that the slope of my red guy is what because it's in y mx plus b form you got it the slope is seven so now could I just simply set up a little expression that says that the slope of the line connecting the two dots would be as you guys know the difference in the Y values divided by the difference in the X values the difference in the yv values would be n minus 0 so we could just write n and then the difference in the X values would be 4 Min - 0 so therefore I'm just going to do n / 4 and what's my goal my goal is to make sure that that value is seven because remember any two lines that are parallel must have the same slope so since that got me a value of seven and that matches the 7 in the 7 x + 5 I do believe we have have our answer and the answer is 28 okay so again it's possible that some students may be able to kind of like figure that all out without Desmos but I just sort of feel like being able to visualize it and um using the tools to get that ever so close then suddenly you realize ah if I really want to nail this I can just make use of the fact that it has to have a slope of seven seeing that there on the display is really going to help uh so the answer will be 28 and we are going to hit next okay guys we're on 22 guess what this is the final boss of module one and then we'll move on to module two um what does it say it says in the XY plane a line with equation 4 yals P for some constant P intersects a parabola at exactly one point if the parabola has equation Y = 5x^2 - 7x what is the value of P okay uh again when you've got multiple things here just hit the gear icon hit delete all and now we're ready to start from scratch first thing I would do is type in the four yal P because we want to make sure that we move that line through the slider P until it hits that Parabola in exactly one point now if we do 4 yals P you're going to notice a problem it didn't give us a slider and it has an error message we only support implicit equations of X and Y so guess what there's a trick you can give it an X but since X is not in the equation just write plus 0x okay and now you're good to go you can add the slider p and Bam there it is and notice that I move this up and down and that makes sense because we essentially have a horizontal line and um yeah it's just moving up and down next thing we want to do is enter the equation of the parabola which was y = 5x^2 uh - 7x okay there it is now what's our goal our goal is to make sure that we move that slider so that it intersects the parabola in exactly one point so I do need to zoom in a bit again this will be much faster when you use a mouse with a wheel and we're we're kind of close right right now it it goes through two places but it's very close to hitting it in one spot so I'm going to continue to move my slider o now it's looking really good I moved it down to negative 1 point Sorry negative 9.8 and again you must do a hard Zoom to ensure that that's correct and I think we're good what do you guys think there's no way that that goes through uh more than 1 Point at this point so what are we going to enter as our answer the value of P which through our slider we know is 9.8 boom done guess what we are going to absolutely Crush that first module and now guys join me as we go into module two okay guys here we are on module two and believe it or not I thought we would start off with number one I know that this looks like a pretty easy question but I do want to let you guys know that um Desmos has some pretty nice statistics features so we are asked to find the median of this set so why not just enter this data in and let Desmos do the work for you okay um because you know they could be sneaky and even though the data in that set is going up from left to right they could have been sneaky and put in some numbers where they're not going from in ascending order but the good news is Desmos will immediately sort the data for you and it will give you the correct median no matter what the data does not need to be ranked from low to high how do we get the median very easy guess what you type the word median okay and then median is a function so therefore it does require parenthesis and then we just enter the data 21 23 uh 24 separate your data with commas by the way uh 25 26 28 uh 32 34 and 37 bam you're done uh whenever you just have a single expression and it calculates it for you it'll be in the bottom so so the answer is 26 and there you go so we're going to hit 26 and we are going to nail that question real quick guys um what if they had asked you for the mean of the data guess what Desmos will also do the mean for you just change it instead of median type mean and Bam the average of that data set will be 27.7 repeating super handy right okay so we're going to pick B and let's move on to the next problem okay guys now we are on number six what do we have we have 28 / 4X + 32 then they say the given expression is equivalent to 7 /x + r where R is a constant and X is greater than Z what is the value of r ah what's going on here well I'll tell you what's going on here another opportunity to use Desmos um anytime they have a question where they say which of the following Expressions is equivalent to the one that they're given and you don't really see the algebra that you need to do or there's some weird trick don't worry you can almost always use Desmos to help you solve it so how are we going to attack this um we are going to attack it by basically taking the 28 over 4x + 32 and we're just going to write it as a function so we can just say y = 28 over 4x + 32 okay um let's hit the home so that we can get better viewing of our graph and there it is there's your graph incidentally guys just a little thing if you don't like your colors because the black sort of merges with the rest of the screen you can change your colors easily just uh hold down and then pick your favorite color okay I like blue and so we can always change the colors if you'd like to so there is the equation of um or the graph rather of 28 over 4x + 32 32 how do you know that you can get the right answer you will get the right answer if it matches directly over that graph okay in other words if it's a direct overlay you'll see exactly what I mean so let's try Choice a and see if R if it were equal to 8 would be equivalent to the existing graph in blue so what am I going to do I'm just going to do y = 7 over X Plus again I'm just using the strategy of testing the answers right nobody says we have to be a superhero and figure out what R is on our own so I'm going to enter the eight and oo look at that guys did you notice something the blue graph disappeared what does that mean it means that since the red graph supplanted it it's guaranteed to be the answer because if I just even were to click the little icon do you notice how it goes on and off it's like blinking whenever that happens it means that they are identical it means that that is the equivalent expression it's the one when R equals 8 you do not need to test any other answer choices that would be complete waste the answer is A8 click the next button and let's move on okay guys here is another question I think this is a super easy question but it's different from what we've done and I just want you to know that Desmos can evaluate any function that you give it by evaluate what I mean is you can put anything you want into it um numbers are a piece of cake so let's just enter our equation G of x equal 6 Plus X cubed again to get the exponent do shift 6 there's my Cube and there's my function and now to figure out what G of3 is you just simply are simply going to type G of three and again because it's just an expression and it can evaluate it your answer appears in the bottom right corner the answer is 33 you're going to pick 33 and you're going to move on all right guys guess what word problems did you think that uh we wouldn't attack a couple word problems with Desmos you bet of course we can do it here we go let's read this one it says the function h of t equal -16t ^2 + 96t + 100 represents an object launched from a platform where H of T is the height of the object above the ground in feet T seconds after it is launched which number corresponds to the height and feet above from which the object was launched okay um I'm going to graph this and I'm going to show you another cool little trick that could be handy in certain situations okay so first thing we do is we're going to enter this function as a rule of thumb uh you want to typically use x as your main variable you can use any letter you want for the name of your function H is fine um however I didn't have any problem when I typed in t so as long as you get a graph you're fine you can use that variable so I think we can use h of T equals and then let's type in this uh equation -16 t^ 2 um+ 96 t uh plus 100 okay and here's the thing there's a lot going on here and there's some stuff to the left of the y- axis which implies that there's some negative numbers but since this is launching an object um and time would be starting at zero and larger we can actually add a restriction and the way you do that is just use curly braces like this and just say t greater than or equal to zero to do greater than or equal you go greater and then the equal sign and immediately makes a greater than or equal sign of course you can use the little keys on the virtual keyboard on Desmos but I find the more you can do by just typing it the faster okay um so we want it to be greater than zero and do you notice how it chopped off the left part of the graph Isn't that cool it just allows us to focus on the more relevant information now it wants the corresponding height from which the object was launched I think you'd agree guys that when you launch the object that happened exactly at time zero so therefore it's basically just saying what is the Y intercept and there it is it's 0 100 and so we are going to pick 100 and that is the end of the problem uh incidentally if they had asked for uh at what time does it reach its maximum height then of course you would click on the maximum of the graph and it would be at uh let's see here 3 comma 244 so in other words 3 seconds into the flight it reached a height of 244 okay pretty useful information let's go ahead and move on to the next problem okay guys check this one out uh this is a super cool one you'll be blown away how how easy Desmos makes this so here we go excuse me we have the function G given by x^2 minus 4 what we're going to do is we're going to type G of X = x^2 - 4 okay and then guess what anytime you do a function of course you can see it right there it is in all its Glory but you can also create a table this would be the perfect opportunity to create a table because all the answer choices are giving you tables those tables are showing you what values of X correspond to the Y values or the G of X values for this particular function so rather than wasting time trying to plug stuff in just let Desmos do the work for you so um hit the little gear icon and then just click on table okay so create table bam look at this nice little table and we can adjust the values for X so that they match the answer choices we don't really care about the -2 the negative 1 do we no we don't so we're just going to type zero and notice that it'll immediately update the corresponding value of G which is -4 and then we're going to put in the two again it's updated to give you a zero and then we're going to put in the four and Bam we have our G of X values are going to be4 zero and 12 and I think you guys would agree that the only answer choice that shows that would be Choice B -4 012 look at that super fast these questions guys once you start to get the hang of it are probably only going to take you about 20 to 30 seconds okay guys uh check it out um we are going to do uh number 12 this is in a module one again um and what do we have we have a cone has a volume of exactly 2 pi cubic in what is the height of the cone in inches so what I'm I'm going to demonstrate here is how even a geometry problem uh you can actually feed it directly into Desmos as long as there's some governing equation in this case of course there is there's got to be a formula for the volume of a cone um just check your reference sheet because remember there's a lot of uh geometry formulas and you see it right there volume is equal to 1/3 Pi r^ 2H perfect so now watch what we can do we can let Desmos solve this for us so that we don't get entangled in any numbers or algebra it'll just give it to us automatically so here we go the volume is 2 pi uh the shortcut for pi by the way is pi so just type pi and that's the volume but that of course would be equal to uh 1/3 so we go 1/3 and then it's Pi again pi and then it's r^ 2 H now you can tell from the diagram that there that the base is two the cone is flipped but it has a base of two but the radius of that circular base would be one right so we just do 1/3 * pi and you know just to make it clear in the formula I'm going to go 1 squar I know that 1 squ is one but we'll still put that there anyway just so you see the formula and what's left is the height now very important um don't use H because if you attempted to it's not going to give you anything use x x is the magic variable so that you can get those pretty vertical lines to represent your solution and Bam there it is okay so it looks like if we zoom in it's going to be six right yes indeed uh every now and then it seems like Desmos will occasionally give you um a nice dot that you can be convinced is correct on the x-axis um and other times it doesn't it's a little bit Whimsical with that but in any case we're sure that the answer is six so you're going to type in six and that is the height of the cone all right guys a brand new problem here that we can easily let desmo solve for us it says 3 * 6X + 11 is 9 * 9x + 4 in the given equation D is a constant if the equ equation has no solution so make sure that you you know even on your scrap paper just write that down so that you don't forget you want it to make sure that there has no solution the question is what is the value of D so in this case you definitely want to look at this from a more graphical Viewpoint so what you could do is say to yourself wait a second I could set the left side of that equation say equal to Y it would graph a line and then I could take the right side of that equation also say set it equal to to uh to Y then that'll give you two lines how do you know if two lines have no Solutions I think we've done this before you have to make sure that they are parallel to one another okay so let's go ahead and type in y = 3 * 6X + 11 all right and there it is okay and then we're going to type in the other one y equals now I'm going to do D it'll give me a slider okay anything other than X and Y that you enter as an equation or rather as a function will pop up as a a slider so that's perfect that's exactly what we want 9x uh plus 4 now we're going to take our slider D and pretty cool right we're already kind of close to um having no Solutions but you see that they do intersect here don't they so let's see what happens if I move my D away perfect and it looks like two almost did the job and what I would do is just keep scrolling a little bit just a double check and I think you guys would agree look I'm already atga 00 they haven't uh got closer to one to one another one bit those guys are dead parallel so you can be rest assured nothing to worry about they are parallel so what does that mean the answer is going to be two because that's the magic value for D that ensures that those two lines have no equation which means that the uh sorry that they have no solution which means that the original equation has no solution when D is two all right a brand new problem did you think that Desmos wouldn't be able to do inequalities now of course it can do inequalities so what are we going to do uh we're going to try to find out which point which is one of our answer choices is a solution to the given system of inequalities in the XY plane let's type in the first one so we've got y less than 2x + six and if I just hit the home button there it is so what that means guys is that the white region the white space any point there would not be a solution anything in that dark brown region is a point that would be a solution to that first equation but we have another one that makes it a system and so now we go y less than 1/3 x + 8 okay pretty cool right so now your second equation is in red and anything shaded red which would be below that dash line would be a point uh would be a point or a solution but we want it to solve the system so a system is the combination of those two inequalities and where do you think that would be if you said yes it's going to be in that dark dark red region you're 100% correct because that represents where there's overlap between the two solutions now how do we figure out which one of these answer choices is correct it couldn't be easier you're just going to Simply test a first and we know how to do points you just do parentheses 8 comma 4 end parenthesis look at that beautiful blue dot it's dead smack in that dark red region which means it would be a valid solution for both inequalities so you pick a and then we move on okay guys let's see what's next we've got a few more to go and we will be done with this video I was hoping to keep it under an hour and I think we're on Pace for that and great job to all of you who have stuck with me through all these problems hopefully you did it with Desmos just like I did now when you see these problems pop up on your first sat I think you guys are going to know exactly how to attack them here we go a brand new type of problem uh again Desmos will handle statistics we've got 355 8912 it says if an integer X is added to the data set above the mean and median of the data set will be equal what is a possible value of x okay so let's go for it um do you remember that we already had a list of data and we were able to easily get the the median of it so we're going to do the same thing however I want to teach you guys an easier way to deal with this data I think what would be smart is to uh put it in a list and the way you do a list is you just use brackets and you then enter your numbers and you just separate them with a comma so go 3 comma 5 comma 5 8912 and there it is and it's pretty cool it confirms that it's a six element list okay just remember lists meet uh must be between brackets now what you should do is it's not mandatory but I would recommend naming it a variable then that way you don't have to recopy the list all the time you can just feed the variable to the mean and the median let's call it a so a is equal to uh that list of data okay um if we were to calculate the mean of that we would just type mean and we will need this so let's type mean of a again you need the parentheses after mean because mean is a function and then we're going to do median also of a now as it the mean is seven and the median is 6.5 however we need to add a value X to this list such that when we do that the mean and the median will be equal so what's our strategy we want to add another uh number and we should do it as a variable now if you do X don't do it okay X is best used for graphing purposes and we're not really thinking about graphs right now we want it just to uh do it purely in terms of the numbers and it's just a complete mess uh I wouldn't even know how to interpret all that so instead just give it um a non-graphing variable the graphing variables of course are X and Y uh just give it B and that'll act as a slider and then you just um click on B and of course you could used any other letter c d uh and so on so we're going to use B and notice that we have an opportunity to slide it don't we okay now we do have to be precise here because this is not um a multiple choice for multiple choice we could just feed those values directly in for B and test them here we have to be exact now I'm trying to move my B value such that the mean and the median are the same right now when B is three for example you get 6.4 for the median and five for the mean uh 6.4 for the mean and five for the median that won't do it will it so I'm going to move um I'm going to move that slider and um it's chopping it off a little bit so so that I don't you can't quite see the screen uh with both values but we're getting close it's 7.1 and 7.8 um let's see here let's just check what it what happened when it was eight okay so what I'm going to do guys just because it's uh kind of blocking the view of both of them let's just expand this and you'll always be able to expand your Desmos on the actual test now we can see everything going on here now it's going to be super easy so 6.8 very close right now and Bam there it is okay when B is seven notice that the mean is seven and the median is seven and therefore the answer is seven we'll put the little calculator back the way it was um and so you will type seven into your student response and you should be 100% confident that you know you got that correct okay guys another word problem and here we go we have an online newspaper and it has 1,642 subscribers when it launches the newsp paper gains popularity such that the number of subscribers triples every 6 months okay so just remember that it multiplies by three every 6 months the formula s equals 1,642 * 3 to the NT power and that gives the number of subscribers T years after launch so we have to be a little bit careful with the units it triples every 6 months but the T in the formula is in years the question is what is the value of n this is an Absol piece of cake using Desmos let's first uh eliminate everything we've done so far and as a rule of thumb as soon as you see like a a formula or something just put that in immediately now again um I would probably um I would probably if you wanted to graph it then you should probably do it as like f ofx um so that's fine let's just go f ofx okay so we're just changing the S to F ofx that's not a big deal 1642 this is very important guys uh do not use commas and numbers numbers notice that the formula in the question says 1,642 with a comma don't put that in Desmos otherwise uh it'll sort of almost treat it as if it were a point so I just type 1642 3 and then we're going to raise it to the power of uh I want n as my slider and I'm just going to use x since I declared it as F ofx but X as you can see is representing my time we're going to add our slider okay and there's the graph which is you know kind of cool um and now how do I know what the correct answer is well what I'm going to do is I'm going to write F of0 and that means that the initial number of newspapers was 1642 and now here's the cool part I'm going to evaluate the function at F of 0.5 now why on Earth would I do that because it triples every 6 months 6 months is half a year and since the t is in years I need to calculate F of 0.5 okay that would be 6 months or half a year later how do I know if it's the correct answer if the F of 0.5 value is three times bigger than the F of zero all right so now what I want to do is just go to my slider and I'm going to change the one to 1 16 let's see what happens when n is 1 16 okay F of 0 is 1642 and F of5 is 17799 I think you guys can tell that's definitely not three times bigger okay okay so it's not a um by the way uh one thing that you should get um familiar with is the crossout tool do you see this little ABC icon up here if you click that you have the option of getting rid of answers and I think that's actually kind of helpful in this case it's not very helpful at all because it just makes the one six look like another fraction uh but usually it crosses it out perfectly all right um so what am I going to do next I'm of course I'm just going to try Choice B so now we're going to see if 1/ half works and if I change it to a half what happens to my f of0 of course that doesn't change um but my f of 0.5 becomes 2160 is 2160 three times bigger than 1642 of course you could check with the calculator uh but it's not okay so therefore we can cross out B and now let's try C I'm going to change my n value now to just simply two and what happens now our f of0 is still 1642 and ooh this looks promising right guys f of 0.5 is 4926 okay incidentally so we let's just pretend we wanted to check to see if that's equal to three if that ratio is equal to three so you don't have to retype numbers you can actually just click on the cell that has that number contrl c and then control+ V directly into the next line and Bam there's your 4926 we want to divide that by the previous value which was 1642 same idea click it it comes up kind of blue hit contrl C and then directly in the denominator of this fraction hit control V and Bam look at that guys it's equal to three so we do know indeed that the answer is going to be C2 how about that that only required about five lines of work in Desmos it couldn't be easier that problem would be very very difficult to try to do any other way by hand let's move on to the next problem okay guys so we have for number 22 when graphed in the XY plane line G passes to the points -63 and 2 comma 1 line H is the image of line G by the way image is just a fancy way of saying that the line got moved somewhere else that's all it is uh line H is the image of line G shifted up five units in the XY plane what is the x intercept of line H let me ask you a question guys would you agree that if we knew exactly what the equation for line G was our task would be a lot easier because imagine you had that equation and it was like an MX plus b form then if it got shifted shifted up five units we would just simply add five to that and then check where it hits the x-axis well guess what we can definitely get the equation of that line do you remember how we easily got the equation when we had three points and we had to get the exponential graph we can do the exact same thing for lines how do we do it very easy type table and enter your data so in the X column you want your -6 in the Y it will be three and then move down to the next row it will be 2 and -1 and those two dots appear here which is kind of cool and now we want to get the equation of the line that goes to those two dots what are you going to type below here you're going to go ycore um 1 that gets you the subscript remember it's uh shift and then the minus sign and then use the arrow to get out of the subscript type shift till day so shift the button next to the number one and then just type M for slope xcore one um and then plus b okay and now check it out if you scroll down do you see it says parameters guess what those are the missing values for the line so in other words the line is essentially equal to 0.5x plus 0 remember uh the slope intercept form of a line is y = mx + b okay so I could enter y = uh 0.5 X+ B which we know is zero so I know it's a little silly for me to write it but that's okay and now remember line H is a brand new line and it's the image of the previous one shifted up five units so what am I going to do of course just add five and there it is it's the red line that just got shifted up once again I can't emphasize enough guys don't just quickly blindly click that 05 because that would not be the correct answer that's the Y intercept so just slide over and move over to the x intercept and Bam it's 10 comma 0 so just enter your answer of 10 that's the x intercept and guess what guys we have one more question to go so please join me for the final boss okay guys here we go uh this video is going to end up probably been um exactly an hour I hope you guys got a lot out of it we are going to do this final question and we're going to call it a day and of course I'm going to wish you guys all a lot of luck on your first sat check this out this is a classic word problem this would drive most kids absolutely nuts by the way this is number 22 on module 2 so it's just you know supposed to be the hardest problem I think you're going to agree that Desmos is going to make a joke out of this problem here we go a beverage dispenser contains 80 ounces of fruit juice the juice was made by mixing X oz of grape juice with Y oz of apple juice okay the value of y is eight more than twice the value of x how many ounces of apple juice are in the punch we're going to nail this it's basically just a classic system of equations we're going to type those equations directly into Desmos we're going to see where the intersection point is and that will be uh that will get us the apple juice okay notice that apple juice is going to be our yvalue and grape juice is going to be the x value so what's the first equation that we could write well we have 80 ounces of fruit juice right and we know that we're using X oz of grape juice and Y oz of apple juice so of course we could write the equation x + y has to add up to a total of 80 okay and there is my uh first equation okay drawn there in red let's get the second equation that's from the second from the third sentence it says the value of y so that would just be Y is that's equals 8 more than so that would be + 8 more than twice the value of x so wouldn't that just be 2x + 8 okay and now we just zoom in and we grab the intersection point and the intersection point is at 2456 which makes perfect sense because those two numbers do indeed add up to 80 and it gives you the correct proportions um to make this problem work and the question is how many ounces of apple juice again I can't I can't emphasize enough guys don't drop the ball at the last minute after doing all this amazing work using Desmos to crush these questions for you make sure you enter the correct number which one is it is it 24 or 56 well since the apple juice was given to us as the y value then of course we need to enter uh 56 okay so 56 would be the number of ounces of apple juice in this punch and of course if they had asked for the grape juice it would have been 24 so there you go guys I hope you enjoyed that takes care of this little video to show you a bunch of questions that you are very likely to see or something similar and I do believe that now you have some really powerful tools that you can use on Desmos to have an amazing test day um with that in mind I wish you all the best and have a great test see you guys

Channel: Cornerstone Test Prep and Tutoring

Views: 6,553

Keywords: desmos, desmos calculator, desmos sat, sat desmos, sat, sat math, digital sat, dsat, sat perfect score, hard sat questions, digital sat math, sat math tricks, desmos tricks, desmos hacks

Id: RbWKMOziQ0Q

Length: 52min 1sec (3121 seconds)

Published: Thu Mar 07 2024