 going to be a series unless I'm really really fast at solving these of the hardest ACT math questions. I'm sure they're applicable to SAT questions as well but I found a source of 21 of the hardest supposedly math questions you would find and as you can see I have a nice ASMR inducing medium with actually some ridges in it that's a that's a cool view we're going to do some math today so come along with me put some headphones on if you don't already turn the lights down get comfortable and put your thinking gaps on or just just that phones either one that's phone curious in the comments which ones you guys thought were indeed the most difficult begin 21 ACT math questions explaining things it can get a little bit tedious and time-consuming and this is the aftermath of about 20 minutes of me trying to explain this first problem and I realized I probably should try to make it through a couple more a quicker pace than 20 minutes per problem with that in mind I won't delve as deep into the explanations so this first question here has an equation and a graph that corresponds with it it says the equation is h equals a times t squared plus b times t plus c and this describes the the height of a baseball a certain amount of time and it was misleading in the sense that it looks like a two well it actually looks like a three-dimensional sketch of what a baseball is doing and you picture it this being night which it is here but you kind of picture this being the distance the horizontal distance when it's really just the time so you want to keep that in mind when we're trying to solve these and think through what the questions asking us so it says if you alter only this equations c term which gives the height at time zero the alteration has an effect on which of the following so I'll go through these one at a time the H intercept and for this one all you really need to know is that H intercept is in fact the height at time equals zero so it kind of gives you that one and that just means that when t over here is zero what height are you starting at what height does this equation tell you the balls should be at and it's this spot right here so next so our answer would be it does in fact have an effect on the H intercept when we alter the c term so it is number one so we can eliminate GH right off the bat now number two the maximum value of Y of H so here we'll reference my little doodle and I drew this and I think I took about 10 minutes to explain that the maximum height is entirely relative to the initial height so whatever the height is initially the ball will go up until its velocity upward as I said as I tried to write here V equals zero at the zenith I suppose you might say sorry I had some company there for a second I forgot I was around explaining the I guess correlation between the initial height oh that's it the velocity the ball initially has a horizontal and vertical velocity and gravity works in a downward force that's what these arrows are here so it doesn't actually affect the horizontal velocity of the ball so the horizontal velocity will stay relatively constant minus air drag and effects like that but the vertical velocity will be some initial position value I mean and will incrementally decrease until it hits the height at which its velocity is zero because gravity is in fact trying to pull it downwards and that has the effect of decreasing the velocity to zero and then ultimately making it reverse direction right at this point at which it goes down to the ground so all that's to say that yes if we change the C term from three I just used that as an example to zero down here the maximum height will not be the same and in fact the ball will hit the ground a lot sooner I suppose you could think of it as you're already starting with you know some amount of height underneath it and once it hits its peak it'll have the distance vertical distance traveled plus all that initial height underneath it whereas if it starts at zero it only has the distance traveled vertically underneath it so yes it it indeed affects the maximum value of H and now that that narrows it down to only J and K so basically is the third characteristic affected the T intercept and I guess this explanation shows that the T intercept would be the point at which only does it return back to its initial position but it if not zero it has to go beyond that initial position and hit the ground or basically I guess the T intercept would be the point at which the height intercepts or intersects the the T axis here so we will think of it as when the height goes to zero because that's where the T axis is axis is so yeah if we change the C it will in fact change the change the value of the time at which the ball ends up at a value of zero so our answer here would be K it satisfies all three of those conditions it affects all of them alright we made it without taking 30 minutes but still took a lot longer than I want to try to move it faster yet relaxing clip number two here real numbers B and C the word problem here that such that the product of C and three is B which of the following expressions represents the sum of C and three in terms of of B all right so all we have to do here is break this problem into components we have real numbers so B C equal real numbers meaning they're not imaginary or irrational let's see rational we know they're not magic three is B so we have C times three which of the following expression represents the sum of C and three in terms of B so we want to know what C plus three is but we don't want to use the variable C we want to use only numbers and B so here you would take this equation and solve for C and then once we know what C equals for this equation we can simply substitute that into that variable right here C should just equal B divided by three and then this becomes B that becomes B divided by three plus three all right so let's look back at our options here just go ahead fold this over B plus three no three B plus three this is the expression we have here and we can manipulate it if I'm multiplied looks like we have a so it's e e would be our solution there right the next next problem we got is for all x in the domain of the function let's see here let's see we got x plus one minus x it says for all x in the domain of that function this function is equivalent to whenever it says that you can kind of ignore that because it just means x can't be zero when you're solving it in terms of itself or you're just manipulating the variables you really don't need to apply that I don't think basically this one just comes down to which of these can we manipulate this into the top one is already simplified but when we have a cube and two of the same variables what you can try to do is pull out an x pull out one of those variables left with so I pulled out an x I have x squared minus one now does that look like something we have I see x squared minus one that's good but we can't simplify the rest of it to one so what I want to do is I see they're looking to see if we remember the difference of squares trick and this one is particularly tricky because it's hard to forget that one is in fact a square of itself in fact it's a cube of itself and it's actually any root any exponent of itself and I guess I just mean that you can multiply by itself as many times as you need and you'll still get one so the difference of squares is where we take this and it's like when you try to what's the word yeah what's that word you try to simplify a quadratic function into something times something else and you get so basically the the rule of difference of squares is if you have a square minus another square or in other words a difference of two squares this can decompose into the roots plus each other and the roots minus each other and you have x plus one and x minus one and then we have we can test that by showing you that x times x so we distribute x to x and then negative one we get x squared x squared minus x and then we distribute that one and we get one times x is x one times negative one is negative one and negative x plus x is zero and we are in fact left with x squared plus one or minus one sorry so that's all to say that this can be broken up into that we our original function the original function says x plus one divided by x times this which we just broke up into these two functions so we have plus one and minus one and right away your brain should go back into basic training with algebraic equations and realize you can sniff out that this equals one so it's like saying one times one over times x minus one where this one is this thing divided by itself so anything divided by itself is always one so we basically just pull this out and we're left with this and I would bet that we can find that on our little sheet here one and looks like it's probably this one if we just go ahead and distribute that x so x times x is x squared and x times negative one is negative x and it looks like those two do indeed match up so all right I think we got time for one more so we have for a project in home economics class Kirk is making a tablecloth for a circular table three feet in diameter so let's let's just go ahead and draw a circle here and the diameter d three feet finished tablecloth needs to hang down five inches over the edge of the table all the way around so I would immediately draw a bigger circle and five inches would be I don't know extra well that five inches so I guess we'll use the little tick marks there and to to finish the edge of the tablecloth Kirk will fold under and sew down one inch of the material all around the edge Kirk is going to use a single piece of rectangular fabric that is 60 inches wide what is the shortest length of fabric in inches Kirk could use to make the tablecloth without putting any separate pieces of fabric together this one's kind of tricky let's see what is this about folding under and sewing down one inch of the material all around the edge is that included in the five inches or is that another inch all around making it six inches should I increase that to six what do I do I'm going to say that it's included in the five inches sorry I think I misinterpreted that because it needs to hang over five inches but he finishes the edge extra one inch of material so so yeah I guess X really is six inches after all see that was that was kind of tricky at least that's how I would interpret it so now if he has a piece of fabric it is 60 inches wide or is that five five feet five feet what is the shortest length yeah basically you want to be able to inscribe a circle and you want the circle to be three feet plus six feet all around our six inches all around which is adding six inches to each side which is a total of four feet and it wants to know the answer in inches so we have 48 inches so we need 48 inches that wide so I would say it's 48 inches let's let me see I got the answers over here question is this one number four yeah it is 48 inches that has got to be the trickiest question wording I've ever come across I really hope they don't actually put that on ACT tests that's ridiculous because they they give you what they call is a width and it's a rectangle so you assume that the if they're giving you the width you assume that the length that they're looking for is naturally longer but I suppose a square is just a special case of a rectangle but I don't know I don't really I think that's some and then the one inch thing that's like if that was someone delegating a task to a person this would probably go down in the history books as the most retarded explanation of what you are looking for ever I think that's pretty ridiculous got some trigonometry next time so questions five and six well we'll dive into that next time alright guys a weird note I'll bid you a good night and I hope you sleep