German Maths Teacher vs. British High School GCSE Math Exam

[Music] so on the daily basis especially under the heart exam series i get asked if i can solve this exam that exam g advanced precision entrance exam etc for myself here on this channel blindfolded and whatnot and through all of these exams sometimes the word gcse does fall i personally don't know which kind of exam this is if it's some kind of entrance exam to university or maybe just higher education in general i can tell you but i decided to give it a try in today's video by the way this video has been sponsored by brienne more information during the video now the main reason why i decided to give this one especially a short is that tom rocksmiths quite a while ago decided to also give it a short 2019 exam of gcse excuse me i have no idea what this stands for i'm just going to refer to it as gcse and he seemed to have been able to solve it during the video and it was a collaboration with ben sparks a subscriber sent me this very video also andrew dodson commented under it i'm watching you my boy and i thought it sounded like fun to give it a shot for myself i hope i'm not going to embarrass myself here i'm hopefully going to be able to solve some of these questions i'm going to look into the whole thing now i'm going to open the pdf up as mentioned before it's blindfolded i have no idea what it's used for or what is there for what kind of questions are going to be covered in there and hopefully i'm going to be able to solve some of the questions by the way if you haven't done so already check out stem to use damage.com my personal teespring shop links down in the description crazy deals going on over there during the advent calendar and now let us dive right in the link to the paper can be found on there in the description as well as tom's video gcse mathematics higher tier paper non-calculator so i'm not allowed to use calculators okay you must not use a calculator okay use black ink or black ball blah blah advice and all calculations show clearly how you work out your answer okay how much time is given for this exact exam 1 hour and 30 minutes this seems like a tough schedule but we are going to give it a shot nonetheless i'm going to let a timer run throughout the whole video and then we are going to see how long everything is going to take and once i start reading through the first question the time is on i'm kinda excited for that let's see how this one is going to work out okay first question here to write trying it's not drawn accurately circle the value of one so we got 6 and 10 and then 15 and i mean it's a right triangle meaning we got 6 squared plus 10 squared is equal to c squared really doesn't matter in our case then we also got by similarity i suppose 15 squared plus y squared is equal to blah blah blah but this really shouldn't matter too much i suppose i mean we can solve a certain kind of system of equations but isn't this just a scaled up version so 15 is two thirds i know three three over two the the first one so um so 15 is equal to three over two times ten i suppose 13 over two good now um okay then meaning if this is scaled up so this right here is just three over two times one squared plus three over two times ten squared is equal to um 3 over 2 times c squared then what we got is 3 over 2 times 6 so this makes 18 divided by 2 is 9. i guess y is equal to 9 and i hope this does work out okay yes 9 is an answer work out the value of oh um is this supposed to be a mixed fraction i'm not certain about that um so we got i'm going to put it here um one whole thing and two thirds but squared i think that's a mixed fraction if i'm not mistaken at least it should be otherwise this wouldn't make too much sense so we got um this is five over two no five over three but the whole thing squared this is um 25 over nine meaning this is going to be two whole things and seven over nines so two whole things and seven over nines okay third question work out the arc length in meters of a semicircle of radius six meters circle your answer okay semicircle so we got a semicircle radius of 6 meters r equals to 6 meters work out the arc length in meters of a semicirc oh yeah so arc length is half the circumference c speed of light obviously is equal to 2 pi r but half of that is just going to be pi r and the radius is six so six pi okay six power i hope this is correct next up circuit diffraction that is equivalent to 4.625 so we got um so 0.625 is nothing other than 5 8 right so 5 8. so we got 4 whole things and 5 8 meaning overall this is going to be equal to this is 32 37 over eight 37 over eight okay let us continue question number five i need to move my board right o dot 0.00097 in standard form what is standard form supposed to mean is this supposed to be like times 10 to the something so meaning 0.00097 is equal to [Music] 9.7 times 10 to the one two three four um negative fourth power negative four negative three negative two negative one no negative five right i hope i didn't get this one incorrectly divided by ten thousand ten thousand yes this should be correct so nine dots and nine dot seven times ten to the negative fifth [Music] work out three dot blah blah give your answer as an ordinary number so we got three times ten to the fifth power divided by four times ten to the third power ordinary probably means just a regular fraction so we got this is 3 times 10 squared divided by 4 but 10 its prime factorization is 2 times 5 so we got 3 times 2 squared times 5 squared divided by 2 squared those are going to cancel out meaning that's 75. okay 75 for number five okay next up number six and i plays a game with ordinary they love to use toward ordinary fair dice if she rolls 1 she wins if she was 2 or 3 she loses if she rolls 4 5 or 6 she rolls again when she has to roll again if she rolls an odd number she wins if she rolls an odd number she loses complete the tree diagram with the four missing probabilities three year year year okay probability that ain't my cup of tea but we are going to go with it and i'll play the game with ordinary fair dice so she's just using one okay so oh there we have the tree diagram already let me let me copy this real quick okay i'm going to copy this one and then one half and then two or three so we need probabilities there and then we got four five and six or six odds and then even okay so i mean if she was a one she went if she was four five six she lose she rolls again if she rolls two or three she loses two or three two out of six is one third and this is one six and if we add these up these are two six three six yes those add up so this works out and then four five or six if she rolls an odd number she wins if she rolls an even number she loses oh yeah so no wait if she rolls a four five six she rolls again if she has to roll again if she rolls an odd number she yeah if she was again all the numbers are back in the pot meaning we got one half i mean there's only two ways to get this one either or even three or three even okay i hope this works is anna more likely to win or to lose you must work out the probability that she wins okay so what are all the paths that she wins this is a winning path she loses here and she wins if she gets she got an odd number whoops so we got this path going yeah that looking pretty fresh so p of win is equal to one half plus no not one half the first path is one 6. this is this one right here exactly and the next one is one half times one half so this is one six plus one quarter which is going to give us um so 12 is the so 2 2 plus 3 over 12 is equal to 5 12. okay i hope this works [Laughter] 5 12. um i hope this was the last one in the probability i think i should take a little break from my miserable existence do you know what always calms me down the contents of today's sponsor brand who are kind enough to sponsor yet in our video here on this channel now praying actually fits right into this video brilliant is going to get you prepared for most courses that you 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something for you then you can try out a big portion of print for free already so definitely make sure to check it out and support the channel this way and now i'm going to punish myself a bit further with the gse exam yes nice okay no more probability i at least i do hope so okay three friends arrive at a party their arrival increases the number of people at the party by 20 in total how many people are now at the party so three friends arrive at the party the arrival increases the number of people at the party by 20 so by 20 okay let me think you can probably do this with cross multiplication most certainly in some kind of way how many are now at the party three so so if if three more people join it's going to increase everything by a fifth right so 15 before then three more this increases the people at the party by 20 no 12 right i mean if we got 12 before and three people make it into the party after that then we are going to increase the number of people at the party by 20 percent yes so 15 people i mean if we got 15 times 0.2 this is going to give us um times oda2 how many people are these um those are two yeah three people yeah okay i hope this is right i'm not doing a simple mistake here i i hope um okay next up so we got 3 to the 12th power divided by 3 to the fifth power and all of this divided by three squared times three so this right here is three cubed this right here is going to give us three to the seventh power meaning three to the seventh power divided by three cubed is going to give us um three to the fourth power which is um 27 times three is eighty one okay oh what is that oh goodness that's that is looking terrible i hate geometry i only like analytic geometry but there's no time for analytic geometry here a shaded semicircle is inside a circle as shown the radius of the circle is 10 centimeters the diameter of the semicircle is eight centimeters how many times bigger is the unshaded area than the shaded area shaded semi-circle is inside circles the radius of the circle is 10 centimeters so we got 10. we are taking a look at the area so the area is pi r squared which is 100 pi 100 per and we now got this boy right here with a radius of four because the diameter is eight meaning the area of this guy is um 16 per over two yeah because it's only half the area of a circle meaning this is going to be 8 pi meaning how many times bigger is the unshaded area than the shaded area um 12.5 times okay because 12.5 times eight power is going to give us 100 turn over for next question okay the number of items n made in one hour by a machine is given by n equals to 60 over t t is the time in minutes the machine takes to make one item the value of t changes for different types of item on the grid below graph the graph of n from for values of t from 1 to 4. okay i mean i can just try to do it kinda accurately one two three four i'm just trying to replicate the craft that i got here so from 10 20 30 40 50 60 70. i'm getting extra points for for drawing once again everything completely just takes some extra time and n of t is equal to 60 divided by t number of items made in one hour okay so from one to four in one hour we got 60 items in two hours we got 30 items in 3 hours we got 20 items in 4 hours we got 15 items i'm not sure if i can connect the points securely okay um just because i mean it's not a continuous thing in normal case b because you can't have half items but if it were a continuous thing then i would connect it okay like like this and obviously it's an exponential decay no not exponential decay i'm terribly sorry it's a rational decay the machine takes three minutes 30 seconds to make one item user graph to estimate the value of n 3 minutes and 30 seconds use the graph i would say 18 18 i mean we have to estimate so i can just make a wire guess here but if i were to take a look at so n of 3.5 this is going to give us 600 divided by 35 which is the same as this so 120 divided by 7 which is the same as this makes 10 35 15. kind of 15 15 items okay but does this make sense no 15 dot something so so around the same number of items that you get for four minutes ed and fey and that was the question by the way ed and faye shared 330 pounds in the ratio seven to four that gives say some of his money fei now has the same amount as it how much does ed give faye okay so seven to four so they split it up into eleven parts so meaning one part it corresponds to um 30 pounds okay the pound symbol this one that i do not write very often so we got um 30 pounds per one part ed gives face some of his money fei now has the same amount as at okay meaning 100 no 156 pounds is exactly the middle point okay meaning if ed has seven parts um he has 210 pounds how much does ed give faye meaning he gives um 35 pounds to faye yes 35 the next term of the sequence is made by adding the previous two terms which of these sequences follows this rule the next term of the sequence is made by adding the previous term two two terms okay so um three okay so we got two plus negative nine is negative seven then we get negative seven plus two is equal to negative five and then negative seven with negative 5 is equal to negative 12 to the first one right yeah to the very first one so we got negative 3 plus 5 is negative 2 then we got this oh second one two negative three and then five negative two three and one two the third one not so so yeah the first the second the third one not and the last one negative one negative one is negative two negative two negative one is negative three and like no okay so the first and uh second so those two from the um upper line the triangular cross section of a prism is an isosceles right tri-angled triangle right angle triangle triangular cross sectional pressure okay the volume of the prism is 102 cubic centimeters use approximations to estimate the value of x you must show your working use approximations to estimate the value of x okay um that sounds like a fun one i suppose so what we got is we got this piece of x x and 8.14 okay so since it's triangular so if this right here is no wait um if we take two of these put together then we are going to get exactly the volume so i hope you can see where i'm going at elementary geometry this right here is a volume of a meaning if we take this divided by two we are going to get the volume of this um meaning this divided by 2 is 102 cubic centimeters this one is 8.14 meaning the volume is equal to 8.14 times x times x length length times high times width times x squared meaning all of this divided by 2 is going to give us the whole volume okay so meaning we got 51 cubic centimeters times 2 divided by 8.14 is equal to x squared meaning that's equivalent to saying we got um 102. oh yeah they are actually going to cancel out the twos as before divided by 8.14 um yes okay so how often does it fit in there 10 times 8.14 is 81.4 meaning what is still missing is 20.6 20.6 2 times 2 times 8.14 is equal to 16.28 oh goodness um that is not too easy to be honest [Music] 16.28 so meaning it fits 12 times into here um 12 times that's not too easy to approximate have i done something incorrectly no probably not it's probably just a question so the whole thing is the volume divided by two meaning what we need the volume divided by 2 oh no no no no wait wait wait wait did uh okay yeah i was doing something weird here um so volume divided by two is already 102 cubic centimeters i shall not um forget that so 100 no 102 goes here meaning that um 204 divided by 8.14 meaning um okay let us see how often it does fit into here 20 times 8.14 is going to give us 160 plus 20 times this 2.8 is 162.8 okay so what is still missing is um 40 41.2 41.2 that sounds a bit better so let's take 8.14 times 5. this is going to give us 40 plus 5 times 1.4 huh still not still not the best number it it seems 41.2 yeah um seven 0.7 0.7 40.7 okay interesting so okay let me think for a second more i'm probably being stupid right here but it just is what it is so we got um 200 so how much is still missing 0.5 so 203.5 plus 0.5 divided by 8.14 that's terrible that is seriously terrible um so this right here is 5 divided by 81.4 so this is 50 divided by 814. no and not 203 it's um so we got it five times 25 25 plus something so let's just go with x is approximately five okay let's say x is approximately five then we got let me check um x squared plus eight dot times 8.14 divided by 2 is going to give us 25 times 4.07 which is um equal to okay 25 this is 100 plus 25 times 0.7 25 times seven is going to give us one dot yeah this is actually good um this is one dot seven five one 1.75 is 101.75 okay this is not too shabby so x is approximately five i have no idea how approximately they wanted but um yeah this is good there here is a quadrilateral um a is 90 degrees and a divided by b is 5 to 3 x divided by y is 1 to 3 show that b is equal to x okay so a is 90 i hate decrease why don't they have radiance here um a divided by b is equal to 5 divided by 3 meaning um b is equal to okay 90 so we have to expand this by 16 18 so um 3 times 18 which is going to give us 30 54 54 degrees okay 54 degrees okay so so let us see i'm going to throw this out so let us split this son of a gun up um so we got 54 here we got 90 degrees here this is obviously also 90 degrees this right here is x and this right here is going to make up meaning we got 3 360 so 180 degrees minus 54 degrees is equal to let's call this one alpha alpha which is going to be the same as 126 degrees 126. okay now we got this right here as a right angle so we got x plus let's call this one beta must be equal to 90 degrees x plus beta is 90 degrees we got 126 degrees plus beta is equal to y so beta is equal to y minus 126 degrees if we put this into here x plus one minus 126 degrees is 90 degrees meaning x plus y is equal to 200 degrees 216 degrees does this make sense so we got 216 plus 54. so i just want to check with my original sketch that i got here is going to give us 270 plus 90 is 360 okay so this checks out but i would have been able to guess this in before so meaning we can solve yeah meaning x is equal to yeah 216 degrees minus one meaning if we got x divided by y is equal to one third that means that 216 minus y divided by y is equal to one third meaning we got um oh goodness 216 minus y is equal to one third well i thought this would be a quadratic but it's not so we got 216 is equal to if we bring this to this side three quarters meaning that's equivalent to saying we got y is equal to three times 216 divided by four 216 divided by four um is equal to 3 times 108 divided by 2 is equal to 3 times 54. what is happening three three times 54 no what have i done to you extra by one four over three what was the value of b oh no we we have to show that x is equal to b i'm being so stupid here now every it it all comes together it all comes together meaning three times 54 is equal to 150 or now we need to hurry the up 162 meaning 216 minus 162 is equal to 54 and now we got it which is equal to x by this equation that we got here yes okay meaning x is equal to b this took so long oh goodness i'm i'm embarrassing myself here oh no here's some information about the test marks here's some information about the test marks of 120 students mark m okay they are bounded in some kind of way and then we get the frequency complete the cumulative frequency table oh um yes okay i think i understand what they mean that's basically just stacking up so m less or equal to 30 those are all the people that have 30 or lower marks meaning we got 48 plus 40 is 88 then m less or equal to 40 is thus 108 and m less or equal to 50 is 120. okay draw a cumulative frequency graph i have no freaking idea what it is to be honest but i think we just have to sketch it somehow and i think it's going to be a discrete graph because i don't know probably because you can't have half students for example so meaning um 10 20 30 40 50 20 40 60 80 100 120 okay 120 this already sounds good meaning 5 120 i hope this is correct and then we have 40 being equal to 108 meaning it's somewhere here a bit less okay i can't do it too accurately but i would be able to do it here so 88 here this is 80 120 88 is here and then what were the other ones um oh no no i assumed i didn't want to assume no no no come come back my mouth i'm so sorry for this um this it's my time away um 48 so 20 40 48 is here and then we got 20 here this seems to be the craft and i hope this is barely correct students who scored 50 marks or fewer take another test use your craft to estimate how many students take another test oh so we would need to connect everything so it probably starts somewhere here okay at zero probably so i can just estimate 15 marks or fewer so we get in 10 here's 20 so estimating this i would say about this is 20 let's go with 35 okay i can just make white guess 30 to 35 something of that sort simplify fully simplify fully um this is number 16. 4x minus 8x squared divided by 12x minus 6. okay simplify fully so um so we can factor out an x here a negative x at that meaning this is going to give us 8 x minus 4 divided by 12 x minus 6. what we can also do is we can [Music] expand this probably meaning negative x is equal to i mean they are just a factor apart basically so the common factor here that we should multiply by to expand the fraction is 16 doesn't work out nicely 24 times 3 no no let me see for a second if i were to factor out uh two thirds we are going to get four x minus two divided by oh yeah yeah obviously so this is negative to x divided by three i think there's nothing else we can do here turn over for next question toby is forming and solving equations the product of half of a number and three more than the number the product of half of a number so x over two and three more than the number so x plus three is the same as the square of the number toby uses y to represent the number you toby how can you ma i'm using x go freak yourself toby let x be equal to uh oh be equal to x it's got forsaken reflexive uh write an equation that toby could form yes should i also oh no i'm not supposed to solve it um toby forms another equation x is equal to 9 8 times 1 over x he wants to look at the value of x here's this working so the idiot multiplies by eight x so what he does is x is equal to nine over eight x is equivalent to saying eight x squared is equal to nine and then what he says no what was the arrow he made so what he said next he implied that 8x is equal to 3 or 8x is equal to negative 3. what did he do wrong well he fallaciously took the square root only on this side and on the x i mean this right here is the correct reasoning at least for the right hand side but he should have used the square root on the 8 2 and that's it here's an identity use identity to work out the value of blah blah you must show your working so we got difference of two squares and we have to use it on this minus seven squared okay then this is 193 minus seven times 193 plus seven which is the same as 186 times 200 oh okay meaning this is two times 186 times a hundred meaning this is the same as um 300 um 372 times 100 so thirty seven thousand two hundred factorized ten i know one one hundred ace okay yeah those are easy ones easy points and i can easily get a bit of time reduction here b squared is equal to 100 so this right here is 10 squared this right here i must show the work so yeah 9 squared so meaning this is the same as 10 a minus 9 b times 10 a plus 9b thank you very much so could a fraction that is equivalent to o dot 1 repeating yes 0.1 repeating is the same as 1 9 because um because reasons abs a b and c are points on the circle c d is a tangent assume that triangle abc is isosceles with ac equals to bc prove that a b is parallel to dc oh for sake oh no um circle theorems like hell i have them in my head elementary geometry i i seriously hate it so we got this this son of a um and we got b c a and d now assume that abc is isosceles with ac being equal to bc so this right here is x and this right here is also x we must prove that a b is parallel to dc um if that's isosceles then this right here is alpha this right here is also alpha um there's probably some circle theorem that that i don't know or that doesn't come to my mind we need to show that those two are parallel a d no a b and d c they are parallel if if they are yeah okay oh goodness that is pretty terrible um i'm not certain how i should do that one i could use analytic geometry but there would be a real time either [Music] oh no alpha alpha this right here is beta [Music] 2 alpha plus beta is equal to when would they be parallel does it help to use angles in this case i mean for for a rectangle or something to be can also look like this now this doesn't oh um i will come back to question number 20. i don't have to solve it so uh 20 is still missing 20 20a in fact triangle abc is equilateral take the two boxes for the statements that must be correct yeah i'm going to come back to this one i can tell you right now i just don't know and i mean i would still pass even if i got one wrong or something um the simultaneous equations so 2x plus 3y is equal to 5p and we got y is equal to 2x plus p give your answers in terms of p in their simplest form okay all right meaning so we got 2x plus 3y is equal to 5p and we also got two x minus one is equal to negative p meaning if we were to subtract these from one another for example then we are going to get three y plus one is equal to six p that's equivalent to saying that we got four y is equal to six p meaning overall that um p is equal to um two verts y meaning if we were to plug this into one of these then we are going to get that y is equal to two x plus two fertile meaning overall that um three y is equal to six x plus two y meaning overall that wa is equal to 6x but we know that y is three halves of p meaning that's equivalent to saying six x is equal to three halves of p meaning that uh um we have to solve give your answers in terms of p meaning um x is equal to so dividing this 3 to one quarter p so x is one quarter p and we got um obviously that y is three halves p this is the one up here okay and p is a constant okay gotcha no not more geometry seriously okay um abc and acdr triangles k as a constant show that the line cd is 6a plus 4.5 b oh vectors right they are vectors k times a three b six a plus seven dot five b okay show that cd is cd okay um um yes goddamn got them trigonometry and so let me see [Music] now my strongest side same with probabilities k a k is a constant meaning that cd does not depend on the constant term basically oh man so what do we have this right here is far this right here is fader but this doesn't help i suppose um three three b six a plus seven dot five b this right here is x i don't see it so 20 and 22. let me come back later okay 20 and 22. um okay next up simplify eight to the fourth power divided by 32 to the two over five um okay let us simplify this is eight to the fourth power divided by this is four times eight to the two over five meaning it's the same as eight divided by four divided by four to the two over five times eight to the two over five meaning this is the same as a to the fourth power minus two of half divided by four to the two over five um oh yeah but this is the same as two so this right here is two times four so this is two to the four times two now um let me try to sort this out a bit better um exactly and this is four to the two over five times two two no what am i doing no no no no this is just i'm just being stupid here right now this was just seriously stupid so let us see um so this is 2 to the third power so 2 to the 12th power 2 to the 12th power divided by so 32 is 2 to the fourth 2 to the fifth so this is two to the fifth to the two over fifth meaning this is the same as two to the twelfth power divided by two squared this is better this is two to the no not twenty-one 2 to the 10th power which is 1024 quick maths okay but this wasn't even necessary oh nice um okay this one seems easy so f of x is equal to i wanted to write x minus 90 degrees because it's sine of x minus 90 degrees which is obviously the same guys so sine of x minus pi over 2 i can't stand the decrease anymore circuit the value of f of 0 degrees yeah f of 0 is equal to sum of negative pi over 2 this is negative the sum of pi over 2 meaning um we got the speech so negative 1 p48 is a point on the circus center o the tangent at p intersects the x's at points a and b show that the gradient of the tension is negative one-half okay showed that the gradient of the tangent is negative one-half so we got a circle centered here we got line tangent passing at point four comma eight and show that the creation of the tangent is negative one half i mean circle's equation x squared plus y squared is equal to r squared meaning four and eight that means four squared plus eight squared is that is sixteen this is eighty is equal to a square r squared meaning r squared is equal to 80. but i don't think that the radius really matters um what do we need to show show that the gradient of the tension is oh negative one half okay so so this tension is some kind of f so f of x is equal to a x plus b meaning if we were to differentiate this one right here we are going to get that um 2x plus 2y y prime is equal to zero yeah radius doesn't matter in this case meaning 2 is cancelling out success of 1 not equal to 0 meaning y prime is equal to negative 1 divided by x and obviously those must be the same okay because we are looking for where the um that the slope is is the same that's the definition of a tension so f prime is equal to y prime is equal to a obviously meaning this is a negative and if we evaluate it at this very point where they meet this is the condition basically we got negative eight divided by four is no four divided by eight is equal to negative one-half okay um work out the length a b give your answer in the form a times square root of five where a is an integer oh oh this is referencing the first one okay um so let me see we got um f of x is hence equal to negative one half times x plus b meaning if we take f of four is equal to eight we are going to get negative two plus b meaning b is equal to ten meaning f is equal to negative one half x plus ten it seems okay this right here is our equation and we need to work out the length a b meaning we got our y intercept so if we take a look at triangle then this right here is our y-intercept this is at positive 10 and now we need to take a look at our zero okay meaning zero is equal to no negative 10 is equal to negative one-half x meaning overall that x is equal to 20 so this down here is 20 ow my neck so we got a length of 20 here we got length of 10 here meaning the distance between the two points it's going to be papa pythagoras 10 squared plus 20 squared which is going to give us square root of 500. square root of 500. how is this bounded that's bounded between so does something between 20 and 25 20 and 25 yeah square root of 500 no um yeah something of that sword something of the sort yeah squared off 500 units i'm just going to go with that okay oh good turning points how are turning the points defined the turning point of the graph y is equal to x plus a squared plus b has coordinate negative to x coordinate so turning point has negative two comma y three one is another point on the graph work out the y coordinate of the turning point okay so turning that's just a parabola right i mean we got some kind of parabola really doesn't matter and f of three is equal to one and this is equal to x plus a squared plus b but x is equal to three so pi i wanted to write par turning point turning point is also the same on a parabola turning point is is the same as the local maximum or minimum so we could differentiate this right so meaning if we were to differentiate this y prime we are going to get 2 x plus a and the turning point has negative two so negative now we can work out no um negative two turning point that's the x coordinate of our here so meaning this right here must be equal to zero meaning overall x must be equal to negative a meaning since this is the x-coordinate negative a must be equal to negative two that means a is equal to two now what yeah x a is equal to 2 meaning um y is equal to x plus 2 squared plus b and now we just need to find out the yeah y coordinate of turning point so we still need to find out the other point so did he have a parameter b meaning we got um yeah so we can use this one up here not too much writing plus two is five that's equal to saying one is equal to 25 plus b meaning b is equal to negative 24 meaning no no no no negative 24 meaning overall if we put negative 2 into here y is equal to negative 24 so meaning the turning point is here oh yeah obviously yeah sure turning point must be at the coordinate b because this is already in its um in its normal form basically yeah it must yeah okay y coordinate negative 24. okay this does make sense oh goodness um english terminology angle x is cubed cosine x work out the size of angle x cosine x is sine of pi over three times tangent of pi over six so that is sun's uh no no that's that's stupid i can simplify this work out the size of angle x you must show you're working no sherlock so no wait um give me a second this right here is sine of two pi over six so this is two times sine of power over 6 times the cosine of pi over 6 meaning cosine of x is equal to 2 times sum squared of pi over 6 times the cosine of pi over 6 divided by the cosine of pi over 6. this is cancelling out meaning this is 2 times cosines no 1 minus cosine squared 2 minus 2 cosine squared of power over 6. i mean you work out how how can we give the answer i don't know i mean just up here it's going to be x is equal to the inverse cosine of two times sine squared of pi over six i mean that's an answer right i mean that is good enough for me at least do i need to show more work do i need to um proceed further here um i'm just going to leave it how it is because that is a totally accurate answer at least in my opinion but you can probably simplify it a bit more kind of but i don't care at this point oh oh okay um let me give 20 and 22 one last try and then we are done i suppose but i'm fairly certain that i would have been able to pass this one assume that triangle abc is isosceles so what was the hint down here in fact triangle abc is equilateral but why must it be equilateral probably has something to do with the chords like i don't know probably some kind of theorem if they are equilateral abs parallel to the seal that is so weird but why must it be parallel i mean if this is an isosceles triangle why do they need to be parallel i don't understand cd is a tangent ah ok scd is a tangent if this right here is 60 degrees and if this other guy is a tangent line then i still don't see how this is the case and i'm going to give up on this question i'm not in the mood for trigonometry or geometry i don't care and this right here is probably something with vectors that i'm too stupid to understand at the moment not understand but i can find a place to start honestly i mean you can probably do some weird sign and cosign and then call it a day but i'm also going to call it a day i'm going to say that i failed miserably here because i wasn't able to complete four questions overall two main questions with two side quests but this was a lot of fun and i'm very curious if i was able to basically get most of the solutions right i'm now going to check with tom's video if i've done well and what the answers to these two questions were that i weren't able to solve right here i haven't looked at the clock but i suppose i was here for about one and a half hours it felt like ages and i think that it's quite a strict schedule but if you prepare for something like this you probably know most of the things already most of the most important theorems this was completely improvised i was just trying my best here and this was higher tier mathematics and i'm also going to look into what gcse actually is i'm i'm fairly certain that it's some kind of entrance exam for university level candidates or something like that but that was a lot of fun i really like this one and if you did also enjoy what you have seen today then why not make sure to subscribe to the channel and to check out my various shops and other than that i think guys watching and i'm going to see you in the next video you

Channel: Flammable Maths

Views: 13,336

Keywords: flammable, maths, integration, hard, university, potsdam, papa, flammy, putnam, integral

Id: zoqv_-3SRt0

Length: 70min 31sec (4231 seconds)

Published: Fri Dec 17 2021