GCSE Higher Maths Exam Walkthrough with @SparksMaths

hello maths fans welcome to the second part of the gcse maths exam video series i am once again joined by ben sparks again hopefully you now recognize him from all of those number foul videos featuring ben that you've since watched from the first of our exam videos as mentioned before we have both completed the gcse maths higher exam we've exchanged papers and we are now going to mark each other's work or in fact we have already marked each other's work is what i should say and we are now about to exchange thoughts comments have a bit of a markers meeting let's say to discuss the questions and of course reveal who got the highest mark though it's definitely not a competition as we both keep stressing definitely not a competition because that would be against the spirit of an exam wouldn't it it would indeed this is why we wanted to record this follow-up marking video in fact to emphasize the collaborative nature of the way that we do maths exams force competitive behavior think a little bit where both of us actually what we're all about is learning maths and doing maths and teaching maths and the competitive nature of exams sometimes kind of gets in the way of that however i agree when an exam happens it's very hard not to get a tiny bit competitive i'm sure you do yeah no i'm i'm mildly terrified about how this is going to go i'm not feeling particularly confident uh and actually i'm intrigued to think to ask you ben how did you find it how how do you think not necessarily how do you think you've done but you know give me your thoughts on having sat the gcse higher math exam it was okay i was worried i was going to find bits of it like way beyond my memory of what i should be able to do but it was okay so that was my sort of overriding reaction but there were bits that stretched me more than i expected and there were bits i found more tedious than i expected um maybe maybe i expected some of it to be kind of dull and some of it is dull and there are bits that i know i messed up like in hindsight i'm thinking i was probably panicking i i'm pretty sure i've got some calculations wrong but it's very hard to i deliberately haven't gone back to mark my own script because i've obviously let the professional do that thanks tom i think it did all right i don't think i would have failed i'll put it that way i don't think so you certainly have not failed i will confirm that right now i don't know what a fail mark is like below 20 or something or no no we've you've done very well i would like to think that both of us were expecting pretty high marks like we should did you feel like it was an easy experience or was it harder than well it definitely was an easy experience but i guess i have a little bit more practice having done the maths a level exam and the further my a-level exam recently in this same context all being recorded and you know throwing out there to the internet me doing classic examples so i kind of knew a little bit about what to expect in that sense the thing that really got me and i've actually already mentioned this to to a few people who've been asking about how this all went is there's a lot of knowledge in gcse maths that you it feels like you kind of learn it just for your gcse maths exam i agree so what i found was with the a-level exams everything there even though i hadn't used it for over 10 years like specifically in an a-level context it was all things that i have since gone on to use at university or i use when i'm teaching every week yeah whereas with some of the gcse stuff it was like i remember this is a thing but i quite literally i learned it for my gcse mass exam and i have not used it in the 15 years since particularly techniques that need maybe if you're going to do it for real which we've both probably done you would never do by hand like this it's the sort of thing that you like you only ever do on paper once and that's for the gcse exam i understand why you have to teach it like if you're going to get a computer to do something you need to know how it's going to do it but there are things i would never want to do by hand ever again mostly involving spreadsheet styles the graph sketching questions like accurate graphs i understand the value of it but i haven't drawn an accurate graph in literally 10 years i'm trying not to comment on whether you lost marks for that or not you use this square grid on the paper whereas i had to redraw it i felt like something i read the instructions which says complete the exam on the exam paper i'm sorry if you missed that line but i had to mark blank paper with your rubbishy sketches but we'll get to that right we will we will on that note in fact shall we shall we reveal the marks i think we should let's get this out of the way i'm really quite nervous and excited at the same time about this i'm just going to say i mean i'll allow you to add your own current in a second i'm pretty sure i know what i've got maybe i'll i'll write what i think i've got in small letters on on the on this page right next to your mark and maybe you can do the same if you like do you have an idea in your head so i actually yeah i've deliberately tried to not count up but yeah you're right i have a pretty good are you going to write in terms of number of marks it was out of 80. wasn't it this page was out of 80 indeed yep so these are going to be the marks out of 80. yours is going to be giant and then i've written mine really small in the corner yeah just so they're saying no i'm not cheating when i'm predicting what i think i got you've put me on the spot though because i haven't thought about this it's only because as i was marking your paper i was spotting where we agreed disagreed and of course seeing the mark scheme at the same time was kind of figuring out what was going on so okay i've put my prediction in the uh top right of my little piece of paper and yours is large with a comment right i'm gonna turn around is that what we're gonna do i'm gonna i'm gonna hold it up and we're gonna like reveal to each other exact same time and hopefully catch our reactions okay i'm already gonna say in advance congratulations ben three two nine competition go oh what you absolutely smashed me right so my exposure is possibly an issue here but uh i predicted 75 plus so yes okay i gave you 73. i would get i thought i'd get 75. it's tiny and in the corner but i wrote something that was my prediction well the moderator's meeting hasn't happened yet so everything yet may change right i can't if it is actually 73 i'm very disappointed i'm not happy with 73. i return it to a percentage right that's over 90 and uh i think in every sort of grade boundary allocation is absolutely smashed the top grade right it's way above level now oh yeah yeah yeah no it's just as usual i'm even more interested now to actually have our discussion about where the marks are won and last to be honest well i think both of us having recently marked a script um it's a good reminder how organic the process of marking a paper is like it's not as black and white as we'd all love it to be for exams right and there's loads of room for discussion so if you can talk me into giving you more marks i'd be happy to go well i think and i mentioned this when i when i was marking i was trying to be generally very generous because i i i thought the best way for me to do this would be how i would actually mark an exam and how i would mark my students exams even though it's university i generally try to give as many marks as possible of course it's always my approach to exams so i felt like that was what i was doing and something else i mentioned when i was doing the marketing um was that um if you got the right answer and wrote something that to me looked like sensible maths i was like yes and just moved on very quickly and i think that's good to go through step by step um i think it even says in the mark scheme that that you can kind of do that particularly if the question doesn't say you must show you're working which some of them do but if it doesn't say that and the answer is correct and there's nothing obviously wrong above it it's pretty much in the mark scheme examiner's advice give them full marks for goodness sake stop wasting your time good okay because that was basically how i was like hazmat got the right answer yes move on like kind of approach well it's interesting that there are questions which uh change that advice and they say in bold you must show you're working and that's when the examiner's advice is a little bit more prescriptive and says look if they haven't shown this step you cannot give this mark uh whether or not they've got the right answer particularly when the answer is given which what didn't happen very often in this paper i think but in lots of other papers i think in your a level one for example there's lots of show that the answer is or yes and then of course it's more about the method than the answer should we shall we start looking at the questions what should we do yeah no i think we we should let's go from the beginning see if there's anything interesting to comment on and and maybe point out where each of us have lost marks i think they're going to be the interesting ones right or maybe where we've used a slightly different method all right so question one was triangles similar triangles i think that was all quite straightforward yeah one mark and attempting to start using pythagoras because it was right angled but not needed that was the only interesting thing about that because they were they were sucking into pythagoras not needed just just yeah as soon as i saw that they both had both had x as the angle i was like i know what's going on here i do want to comment before we get too far into this that you did choose to do it on plain paper which i think did put you a disadvantage in terms of marking because like circling an answer when it was given a multi-choice you had to sort of write it no that's not bad slowed you down a bit perhaps and also well we'll talk about the graph sketching won't we yeah we will indeed um right the next work out the value of this uh question two yeah what was that yeah you just turn it i can see here you've turned it into a single fraction squared it and the guy did the same thing i think you did too the my overriding feeling about this question was that i hate mixed numbers but i think they should be never used again in every other circumstance where you write for example the answer was two and seven ninths uh but you write two negative seven nights that should be two times seven nights in every other circumstance algebraically everything and so mixed numbers get my goat i would get pretty upset about them uh okay the one here that i think i didn't get confused but i mentioned this was that um i wasn't entirely sure whether it wanted the arc length or the perimeter yeah specifically i mean like even though it says arc length yeah but what does that mean does it mean the whole shape perimeter because it could do and i think that that's the thing you're saying about gcse like requires some knowledge which is quite specific and maybe not applicable any time afterwards we need to know what they expect and that it's rewarding that like but although it does say the arc length of a semicircle and i guess like so i had the same debate and i eventually decided if they wanted the whole lot they'd have said perimeter and that was my only form yeah yeah yeah no that was yeah yeah but you got you got full marks on that we've both got six pi and that's that's a relief i have to say uh then we've got decimals and fractions haven't we yeah so circle the fraction all right again circle it and you had to actually go and do it but we both turned this into a fraction i think wasn't it i took a lot longer on this than i should have done but i was at that stage of panicking of like i've got to get these easy questions right or tommy's going to roast me and how he has every right but i think we always got the answer i'm not too worried about it they're frustrating skills understand why they're being checked at gcse though but they are sort of skills that we forget to practice because hey true yeah you're very true if we use a calculator no one's going to tell us off question five nine point seven times ten to the minus four yep well done ben he knows what standard form is another mark i had a lot of fun with number five i had to really rack my brains for what standard form is again there's another bit of vocab that has a very specific meaning that you've probably not used in a long time but if you're a physicist you probably would have done that's the like if you're dealing with irritating units and lots of different things all the time then that's why standard form ends up being useful but do you have a definition now do you are you happy having done it i think it's just the is it like you you use two digits and then it's like something points some like one digit point another digit would you just give two digits times ten to the whatever is that how it works i think it's got to be a number this is this is from top of my head and i haven't looked this up recently but a number between one and ten yeah yeah yeah not inclusively or one to nine point nine recurring oh hold on let's not argue about that one times a power of ten multiplied by a power of ten yeah i remember the power of ten i just wasn't sure exactly how many like numbers you were allowed so it could be for example it could be like three point one four two eight six times ten to the something yeah yeah you can have as much precision as you like in there gotcha um but it's got to be in the form of a number between one and ten times apparently okay i think anyway we both got the right answer so something yeah yeah yeah sorry uh the next one uh so you did this slightly different to me i can see so you've taken the three quarters times whatever tens were left whereas i multiplied out the top multiplied out the bottom and then cancelled the zeros yeah so you just turned them into the the three hundred thousand over four thousand cancelled everything out you got three hundred over four which is where i started panning is like wait can i do three hundred over can i do that um that's the bit i'm sure i got things like that wrong later on i'm sure i did but but yeah so i i kind of treated like the whole thing in standard form i got the three quarters although that's not technically standard form because that's not above one right anyway um but i knew the powers of ten whereas you just kind of ditched all the standard form and it worked out fine and that's as long as you've got some sensible number awareness this is the sort of thing where the method doesn't matter just be sensible about it yeah yeah exactly especially when it's only a couple of marks as well ah anna and her game i remember anna question six was the first longer question a probability question although it was it seemed to be more about the artistic way of drawing a tree diagram than anything else but [Laughter] i i spend like two minutes right like basically writing out what's happening and then in my head i'm like i'm clearly gonna need to draw a tree diagram and then i scroll down and i'm like oh they're actually oh they're asking me to do that yeah yeah and again massive advantage of having being able to write on the paper which the students do in the real thing whereas you have to draw the whole thing but a lot of that works so just in terms of time actually better to work on the paper but hey to be honest you did you did fine well done um yeah so we just figure out the multiplying the events because they're all independent seemed all right and then it wasn't clear to me a though what they were after it said the four missing probabilities now the only reason i knew what to write were there were four sort of lines on paper to fill them in i wasn't sure if they wanted me to fill in the probabilities at the end of the branches i i did as you may have noticed because you kind of needed to remember the next bit right exactly i guess yeah yeah i i interpreted that as just the ones on the branches like you say where those gaps were and then obviously there's part b was checking do you know how to read one ie independent events multiply together and actually i i well i'm just going to show a glimpse of your working here look uh this is this is your tree diagram very finely drawn thing here but i really like the fact that you did the first part in black and then the bits you were calculating for part b which we haven't talked about yet you did in red and that really helped me as a marker know what to mark so so i commend you for the change of pen color that because i'm a human being trying to figure out what the hell you've done it helps yeah yeah to be able to separate that so that's good so yeah we just had to get the four totals didn't we two of them were losers two of them were wins yeah add them up and we figure out that the lose was more likely but as it says you must work out the probability of winning during that process which was five twelfths in the india to add the two outcomes uh there's lots of additional guidance given in the mark scheme it's gonna be all of that because you got it correct it's fine so i found something interesting that the mark scheme for this has two pages of alternative guidance oh this did my headed on every question i was like right ben's got it right scroll down oh no there's another page oh no there's another page of alter like when you begin to see what a nightmare it is for examiners to mark scripts where they basically have messed everything up but there are sort of all these conditions of like how you might be able to ward a method mark because they've done something right i think in the same spirit as you were saying earlier that examiners actually are trying to be as generous as they can and it would be horrifying if they weren't to be honest they would be just really mean but at the same time they've got to mark thousands of scripts thousands and thousands of scripts and have them sort of have some measure of equality even though not everyone's marking them so so that ends up being really prescriptive and it's super daunting uh as it happens marking our scripts i think was a lot easier than many scripts because mostly speaking for myself it was correct uh but it's when things go wrong and how you can still award marks it gets really complicated in the alternative methods um and i think this is the first question where uh it was kind of like a show that question wasn't it wasn't quite because but but you had to sort of construct an argument about whether she's more likely to win or lose and i feel like there were lots of mark suddenly and it wasn't just a calculation he had to come up with a conclusion which is nice i feel like that's that's what probably questions before it's not just what is the probability it's then what is it right and it's two marks right well it gets the two marks they've made that so much more difficult than it should be in the mark scheme not the question question was fine anna and her games all right oh i enjoyed number seven three friends at a party yeah i think i made this one so much more difficult than it should have been well i feel like i did even more than that you did a really simple when i was marketing it was like oh that was easy and i remember sweating a little bit over it yeah i i don't know if this was just me because i feel like these kinds of questions about proportional or percentage increase it's like you know how they work or at least we do as mathematicians but they're very easy to just it just feels like it's so easy to fall into a very slight trap and mess everything up so i think both of our instincts and questions like this are to jump into algebra whereas nothing in the question mentions algebra and you imagine that students who are sort of algebra shy are desperately trying to figure out well if it's gone but this but it must have must have tweaked by this amount was actually the algebra just codifies all that and you stopped worrying about the context and you solved the bloody equation but your bloody equation was much simpler than my bloody equation because i had like uh their arrive three friends arrive their arrival increases it by twenty percent in total how many people so i was like well if x is the number of people then x plus three is the same as x times one point two yeah yeah and whereas you were like well twenty percent's a fifth so a fifth of the table must be three must be three i'm like and your entire multiplication consisted of like five times three and that's and then well that was what yeah so that was i did then i did then double check it using your method so in the actual video i i sort of talk out loud about checking it because it's yeah because as i said i i always double check things like this because these to me are obvious things to just make very slight slips yeah whereas i uh on my algebra on the paper that had had to do three divided by point two oh like three divided by a fifth and i was thinking yeah look i'm fine with that but it's a really potential massive problem for people who are uncomfortable with dealing with fractions like the yes the calculation i ended up having to do i can imagine a lot of gcse students who are not feeling confident just crash and burn and i don't blame them right question uh powers of threes playing around with them this one got me the fact they put the divide side like i hate their device yes it's up there with mixed numbers for me actually i had to go and look it up do you know what that symbol is called i'm going to get there i think it's called side yeah well i would call it i think it's called an obelisk obe lus and i like the fact that i didn't know what it was called means obviously that nobody ever uses it or no one should because all it does is make calculations ambiguous right and messy i agree i agree luckily they put enough parentheses in here or brackets to make it not ambiguous so i wasn't just like cursing the world yeah yeah yeah yeah when i first saw it i was like is this one of them where it's like only genius console like a level of uh can we not do this please crappy viral maths on the internet hey go and read kyle evans book about that one i'm sure that's a word but we've both got this right and we both just um interestingly we both rewrote it without the division signs yeah that's right fractions canceling your yeah it's just working out it's working with powers isn't it the rules of powers that's basically what the question was and like a bigger piece of advice is get comfortable with fractions if you're gcc student your actions are your friends get comfortable with them because they'll make your life better believe me even if they're scary right they're just better oh they make this so difficult right 81 thank you so he can have three marks because he's done that in a sensible way fine i don't know how much you're supposed to follow the exact mark scheme here but if i'm seeing something sensible and ben has the right answer i'm giving him the marks i hope you're being as nice ben just gonna throw that out there right if your answer is correct and what you've done looks good i'm giving you full marks please note because question nine uh was a diagram indeed which you had to redraw yeah i think we we both i'm guessing i remember getting 11 half i'm assuming i got full marks for this one you've got full marks uh yeah none of your marks have been lost so far although on the recording of the marking video question eight i did award you only two marks but only because i didn't realize it was out of three i clearly thought question eight was only worth two months at the time okay so there's gonna be other errors i'm gonna look out for all these errors now yeah i had to go and resurrect like 73's too low i'm not happy yeah well i am going to be the first to admit i'm not a perfect marker i'm mostly perfect but yeah there may well be arrows so let's find them if we can because to be honest i would expect better from tom crawford i'm just um right so this one was um i think we've both done it the same you work out the area of the semicircle you work out the area of the whole big one and then obviously subtract off the semicircle and then you've got your two areas compare their ratio one's eleven and a half times bigger than the other exactly yeah so there was a there was four marks it felt like it was quite involved and i was thinking i think a lot of g6 students are gonna stumble on this because there's a lot of bits to do but it didn't feel like a silly question it just felt a bit like why why why do i need to know how many times like i feel like it's easy to ask questions why i need to know the area of the two bits maybe it's from manufacturing or something but why the ratio and then it wasn't a very nice number which is the first like that did gcses have bad numbers in the answers exactly i always say this to my students like if the answer is i don't know 19.7352 probably something's gone wrong in your in your calculations no anymore no i think there's there's more and more like there was another one later on i think that where the answer was like yuck if i messed this up and i don't think we had question 10 right now i noticed ben actually used the square paper so has an accurate graph unlike me if we remember graphs first of many of me attempting to draw bad graphs okay i'm going to warn you this is the first minus mark on the script i okay i am going to say that i completely disagree that i get a minus mark on this but yeah well i'll we'll see we'll see i'll justify my thinking and if you can talk me into getting the mark back and we'll see what happens so it was it was a graph a reciprocal graph 60 over t and on the grid loads draw the graph i mean first of all thomas said on the grid below i don't know where your grid went i i couldn't explain this to you i couldn't figure out how to draw on the pdf so i had to draw on a different app i was i would have drawn it on the obviously you've said yourself i was adding extra like sorry difficulties for myself having to redraw everything i'm not going to give you bonus marks for being difficult all right but i do appreciate it it's actually much harder to do without that grid there so it's really important actually gcse gave that grid because drawing a graph a sketch graph from scratch actually i think is a good mathematical skill to be able to from nothing get an image of what the function looks like which by the way you did very well i'm proud of you thank you so i did get the two for the drawing then no uh and i'm gonna cause it says do it on the graph or no no i'm gonna quote you the mark scheme now um oh here we go should i show you i'm gonna show you the mark scheme i'm gonna put up my graph's really good i'm i'm not happy about this i think my graph is excellent considering i i felt like there was enough black and white instruction in the mark scheme for me to i didn't have a choice are you seeing the marketing now this is question yes yeah we can see that uh and there were two marks available there's a method mark um n stands for method brother and ace a for accuracy i got used to thinking that was answer mark but it's accuracy right um and it said plot the points blah blah blah blah and uh i believe just having a quick look at your work so everyone can see are you seeing that uh you did put the points and i gave you the m1 mark i think so i then look back at the mark scheme and it says a correct smooth curve through the correct four points that's for the a1 so this is the mark uh that i had to look uh this is what killed you i'm afraid the curve should be no feathery i'm so not having no fear i'm just gonna show you your graph again i'm gonna zoom in you have shown me the correct phrase it does say that i can't that it has to be a single smooth one and i think if you just feathered it a bit i would have been like i know what he's doing fine or or if you'd just done two lines but because it was kind of feathering and more than one line i'm like if i was if i was doing this for the exam board i would get pulled up by the lead examiner but not mocking but i also feel terrible that you're not getting a mark because what you then did was used your graph as they said to get an estimate and because you'd done it on paper it was a sketch graph and you got exactly the same answer as me on the printed graph i feel like well fully justified however i just thought it would be a good discussion point because uh any student doing that would lose a mark and i kind of hate it no that no i i i'm i'm still unhappy but i completely agree with your marking actually um yeah i hadn't even thought that that would be a thing but it i guess it's a valid point because the question is about like sketching or drawing a curve and i have i mean i do this all the time when i draw graphs i never just draw one line i always do it several times because i'm aware that it's a sketch and so i just want a rough idea of the shape exactly and obviously yeah what's crazy as well is it's asked for a value of n at the end and it says an estimate but like it doesn't really communicate how much of an estimate it's going to be like plus or minus two or three based on the shoddy nature of line drawing and stuff exactly yeah but hey uh so i don't think you deserve to lose a mark but the mark scheme says you did so i'm sorry all right no problem uh but then we both got one obviously yours yours does have a nice single line well done and then we both got the the estimate didn't we the 17. yeah i did try to do it a different color just to to make sure that you were noticing although i didn't use a ruler um to draw my lines because i'm i'm working on a screen and things and yeah anyways it still works yeah oh god this mark scheme is worse than the exam i think the answer's going to be 45 yes and he's done something sensible there he has done something sensible all right three marks nice i think we both when i was reading your solution i was really happy to see that we both immediately looked at it and thought we need to divide by 11. oh look 330 perfectly divides by 11. it was a relief was kind of onto a winner from that point i found this question surprisingly non-intuitive at first but but it does feel like the sort of thing you argue about someone with in a pub like you you paid for something and you're like you're just going to sit about who knows what and you're like so actually i kind of liked this question because it didn't feel like learn the method and do it you just got to sort out what do you offer or whatever it's a good like real life example yeah yeah i i agree i thought it was a it made you think there was some interesting maths ratios division etcetera i thought that was a good question happy with that one and we both got we both wrote down a similar sort of style like uh we got it down to 210 and 120 uh for the for the seven to four bit and then both wrote down like as if by magic the number 45 because we could see that that's the bit you sort of like tweaking it yeah one six five each how did you get there yeah actually it was one six five we won't growth there and then and then 45 appeared in both of our working um yes but there's a lot going on on our heads to justify that luckily it didn't say uh prove how much like or show every all the steps so i don't think we could go mark down for the slightly non-linear way of thinking anyway we both got it right and that was a nice question i thought uh sequences oh i enjoyed this one because i just i don't know if you did the same i just checked the first one first it was like oh it works and then quickly check the other sphere yeah yeah at least the first one was right you feel confident like well i think that's going to be the right answer and the rest is just a check-in exercise um it was interesting i did spend a little bit of time thinking about why they put the other sequences in like what were they trying to catch them out with if they were not it was the pluses or minuses yeah it was yeah and the question is hard because of negative numbers isn't it it's a uh it's testing whether you're comfortable enough with negative numbers which is a really sort of normal thing to be a bit uncomfortable with that they're a bit confusing at best yeah yeah yeah hey but you did fine well done i think i'm super patronizing today i'm not meaning to be really well it's my turn to be patronizing because it's ben you did not get full marks on question 13. i know and um what did you do wrong ben well i haven't marked it but i'm pretty sure i did some brainless calculation issue but i'd love you to explain it wasn't brainless but it was a calculation issue so what's the question was uh volume oh it wasn't the volume of a prison it was this question got me actually you had to estimate yeah because of the estimate and again i think that's a gcse command word that has a certain meaning that i i had no idea what it meant to be honest tell you what so let's look looking at yours well done i gave you full marks what you did was wrote down an equation that uh calculated the value of the the volume which we both did i think exactly with the exact numbers yeah times 8.14 has to equal the volume we're given which is 102. yeah and then you did uh you halved 8.14 maybe should i put this on the screen it's easy to still work it through there so uh you half 8.14 to get that and then you divided by 4.07 and then you square rooted and only at that point did you start estimating and the mark scheme the first method in the mark scheme was a bit surprised about this because the first method was like they should estimate all the numbers and then it'll be simple calculations but there was one point in the mark scheme i think that said if you see that calculation that 100 over four at some point then you can give at least one of the method marks and maybe two and so i saw at the end i was like well that's a relief i can give him full marks and then i saw the five and i was like my memory was like ding ding ding wait a minute i don't remember writing five this question so what so what did i do so what you've done is you you did do the estimation at the beginning so you've got a half x squared times eight equals a hundred i decided that i thought estimate meant around everything to one significant figure which rob eastaway uh he did a number five video about it he said look let's call it the zekel's method if it approximately equals uh just just do everything to one significant figure all the time and everything will be simpler and you'll get a pretty good to one significant figure exactly yeah that's that was the rule i decided but i yeah so no that was that was all correct and then you said half x squared is 100 over eight and then you said x squared is 200 over eight and you simplified that to be a hundred over four so you got down to x squared equals 100 over four which is all in the mark scheme and is all where you should be yeah and then for some unknown reason yeah you wrote answer equals 12 and a half and i have no idea what happened between x squared equals a hundred divided by four i think what you've done maybe is divide by two i think you've done two x so i had to square root didn't i so i hadn't done the square root by that point so i'm now looking at my answer thinking 104 and then i think i must have been panicking right under pressure or something think trying to go too quick and i reckon i thought 100 over 4 is 25. yeah no i think i got the 25 from 100 over 4. and then yeah kind of forgot that i'd used the four and thought oh but i'm square rooting uh so the four became a two when i square rooted oh i see but then okay fine it's just nonsense yeah it was a bit confusing but i you get you got two out of three i believe according to the mark scheme though because you made the approximation yeah and said i think if you wrote x squared equals 100 over four you i think you got two out of the three for that point yeah there's m one for anything being rounded it looks like yeah maybe uh maybe i put this on the screen because it's interesting how easy the marks were to get right even if you messed up as badly i did if i was being completely honest if i was marking this without a mark scheme i feel like what you did would be worth one out of three i agree it was that sort of like stupid really it wasn't stupid but it was like you know it felt like you were quite a long way from like the key part of the problem was the square root so yeah and i didn't turn way away from i didn't check the answer either which would have been a major red flag like something's wrong common earlier that you check your answers flipping out but i would have got one method mark for any of those roundings there which is quite generous and then another method mark dependent on the first one as long as i don't something rounded for exactly any of the calculation construction really and then the accuracy mark we're getting fast as long as this case as long as you've got both method marks the thing for me that i think actually this might explain i'm trying to make excuses now but might explain my irrational blip there was that i was super relieved that we've gotten x squared equals two square numbers so that yeah when we're going to square root of like it's going to be possible otherwise what's this doing on a gcse it would be like square root i got yeah which it is it's 10 over 2. yeah otherwise known as 5. but more on over here deciding decided yeah there's only one but we both lost one so far they're scaling when you lose a mark to realize how how tiny slips like that just lose you the marks but you're right we've only lost one mark each so far so i think that's a good question although i dislike the sort of blurry um what does estimate mean and actually i need to go and look at what they actually want them to do other than just do something sensible which is maybe the best interpretation of it first mark dropped question 13 though pretty good going ben well done um right 14 but he did get two out of three even got wrong answer so important to show you're working everybody so question 14 was a quadrilateral a lot of fun with this in the video there's just loads of clips of me going i'm sure the angles have to be 360 degrees i'm sure that's a rule like i couldn't remember whether or not it was i now know it definitely is but i was like i think that's right well interestingly i wonder if we could come up with like if this is what's true about maths in general i think is that you can get away with doing maths gcse particularly if you learn lots of stuff but yeah in both cases both of us at this point we're a bit unsure i think about oh have we learned that but the nice thing i feel about math is that even if you don't learn the stuff you should be able to convince yourself of the truth mostly even if you didn't learn it right you can almost derive it from scratch so yeah how can we convince ourselves that a quadrilateral has 360 internal angles any thoughts um oh i just thought about um the the pattern that happens with shapes so i know that there's like the general pattern of five sides being 540 six size 720 based on a pentagon a regular pentagon is because he knew about pentagon yeah i knew that i knew the total of it hexagon was 720. so i just began to see there was a pattern for the regular shapes and i felt like similar to that triangle you i feel like everyone knows the triangle's 180. i was gonna say that's the fact that i feel like we've all learned right and we also it all sticks with a lot of people doesn't it that one's stuck in your head so for me yeah i don't know just it generalized more and i was like well you know you've got an equilateral triangle which obviously is 180 but it's true for all of them you've got a square which is 360. it's probably true for all of them that was kind of how i rationalized it in my head and what's nice as a marker then none of that uncertainty that you were feeling live came through because you just literally wrote down total equals 360. uh obviously true clearly true facts use it and and then we had to prove that beagles x which worked out they're both uh they're both 54. there was a lot to do here for three marks there was a lot to because you had to do the ratio bit at the start you did the ratio to get what b actually was yeah right figuring out the you know it was 3 times 18 yeah we both did that slightly different but we got there and then you had to spot the relationship between x and y and then you needed the total is 360 and then you solved for the actual exactly and it essentially be the way i did it i had calculate b and calculate x and then they happened to be the same number it didn't feel i felt like maybe there was a way just to show they're the same without needing to know their number but to be honest i was so glad that they were the same number i was like right that was how yeah yeah yeah i went in the same thing i thought i'm going to calculate b because i can see how to do it can i figure out x yes they're the same yeah rather than trying to use an angle theorem or something i'm going to say one more thing about the quadrilateral being 360 point because i was really relieved when i had this exact same doubt like oh yeah is it is it 360. and i fell upon what i think is actually a neat way of justifying to myself because i knew the triangle thing like you just said i know the triangles have 180 and i feel super confident about that in fact i'm sure i could prove it but i didn't feel like i needed to and then i just realized oh it's quadrilateral you can divide it into two triangles two triangles [Applause] yeah yeah and like but the same way for any pentagon i can get into three triangles and then i know the pattern going on and i felt happier at that point to write down my equals 360 equation but it's amazing like the the self-doubt you get in those moments basically under pressure the gcse pressure yeah anyway full marks both of us so i think we're all good on that draw the commutative frequency graph again he's actually using the square paper so it's actually accurate stats question hey did you love this as much as me it wasn't that bad apart from i'm gonna guess do i lose marks again for drawing a bad graph you did not lose marks on this question yes [Laughter] okay i learnt my lesson five marks available um you did do a graph and i was having realized i was feeling guilty at this stage for docking you the mark earlier i was like but if i've done it once i'm gonna have to do it again and i looked very carefully i'm gonna show everyone again this is this is the graphic we've skipped on to uh part b really but part a was just adding up some numbers right was it um yeah complete the cumulative frequency table add up the numbers well done we all did that correct which is a relief yes but your graph is actually really nice it was a single line and it was not feathered so i'm like have two marks okay good and even better because you didn't need the paper to do it that said we ended up with very different estimates when we used the graph and i think that was purely down to the fact that your scale was necessarily hand drawn and not of course yeah yeah but um interestingly again the mark scheme allowed for that it just said use their graph yeah as long as they've read their graph correctly whatever their graph is yeah i feel like yours yeah now i can see that your answer is is 32 and mine's 40. i feel like yours is probably actually what the answer should be yeah but then in the market they don't even say what the answer should be all five points plotted smooth curve or polygon interesting they could have done straight lines uh would have been fine according to mark's theme yeah and uh 15c correct reading from their graph perfect that's it yeah and i was like well you're gross tiny bit of but didn't lose any marks ouch and the only in the sense that uh it was the graph that i would have drawn on a piece of blank paper as well and it suffered from the scales being not super regular not perfect yeah yeah yeah but from your graph i would have nailed 40 as well so you got full marks well done i'm being hyper critical but it's nice to see that the exam guidance is that prescriptive and they know how to give marks if something slightly unusual like if the student didn't bother doing it on the right paper sorry i'll go i'll stop going on a minute man right 16 some simple guy uh simplifying um an equation so you just have to spot the common factor didn't you in the top and the bottom yeah what's the answer what's the key uh minus 2x over three yeah does that know what i wrote i don't know i don't remember what i wrote oh no way no way i'm not gloating is that is that on the mark scheme you actually have to simplify that do you want to see the question again no no it does say simplify fully it doesn't say specifically say it has to be too easy if the question is said fully i mean that's a big mistake from me i know i should have i obviously should have done that but i think i probably got too excited by the fact that you were cancelling the b the brackets counter really nicely is super satisfying and that's what we all live for isn't it in fact i think i can't remember if i've watched this bit of your video but we're both time for me when i got to that question after the stats question which was a bit uh and i sense the excitement in your answer you got so excited but the mock scheme is on screen now and you see the accuracy mark is given only for the two and the three there's no mention of that you see the method mark is given for the four six method it feels like that's much more like the mistake like it's it's a sort of blip like too excited moving too quickly um the feathering mark i agree was more controversial it's hopefully the kind of thing that both of us would have spotted if we'd have used the additional 30 minutes we did have yeah yeah to check our answers yeah absolutely and uh the additional guidance for that was was quite explicit it's like you could you allowed negative 0.6 recurring if you'd gone decimal as long as you did it yeah um correctly you could have got that but because your fractions are your friends you stuck with fractions yeah it's just a shame it didn't say simplify fully it's the sort of mistake that really good gcc students would still make and it's frustrating but they'd only lose one mark like you did good old toby in his equations enjoyed this one uh right it says solve this question mark hmm not sure what's going on there ben i mean are you asking me to solve this as as the marker 17 was fun uh how you kind of wrote solve this question mark i made a comment when i was marking be like wait am i supposed to do this for you ben are you asking your marker there's a challenge answer the question like i um i watched your opening this because we i think i watched this segment of yours a little bit just to see how you got on but both of us commented uh question 17 we both read the question toby it's for me and solving equations and both of us are like well done toby yes good behavior toby good for you um it does beg the question why uh and because he never got to solve it i'm like was that as far as he went you just yeah yeah yeah because it said he was forming and solving them but this one he only formed and that's why i wrote so obviously he tried to solve the next one didn't he yeah i feel like it seems odd that you form the equation in the first part it should feel like the second part should be then solve that equation yeah i agree they kind of anyway i wonder if the first draft of this it had something like that and they just got edited out may who knows maybe but it was an easy two marks i think for both of us there and then part b was the classic mark someone's error yeah yeah yeah i do like these questions i think they're hard in an exam uh but they do test understand for one mark this this was probably the toughest single mark question on the paper like i think what i'm glad i think about it is that the fact that these questions are now more often on gcc's they didn't really used to be this is like testing a bit more of a problem-solving sort of big picture thinking but because they're on there now it does give a much better excuse for teachers at gcse to do this sort of exercise to to make people pay attention to what misconceptions are likely to happen and i think that's good pedagogy and the exam is actually backing it up auto often exams make you just learn stuff but this is rewarding familiarity with misconceptions which is a great thing i think and yeah i i think we both wrote the same answer we both wrote something about square rooting the nine and not the eight he forgot squaring the x and not the enemy yeah but the mark scheme didn't actually that it was not in any of the guidance for the marxist i was hunting through and eventually i found something which basically just said look if it's a correct comment give them the mark and i'm like yeah your comments correct but all their all their example responses um were things like he has taken it as 8x squared like in brackets which would be uh or he is divided by x instead of square rooting which would have done the same effect and like yeah um and he suddenly realized there's loads it's the root eight he's forgot to square root the a that is the value it's interesting that we both interpret it like that and the mark scheme doesn't there's literally like tens of example comments uh some of which get married and none of which we wrote and well some of which don't get marks like one of the example comments is he didn't divide by eight and it was like well yeah he did apparently if they write that don't get a mark it's always fun to see the example comments where it's given zero it's like the examiner's like more on here's a more on it you know he's a teacher he spots the mistakes very good um right number 18 um oh what were we doing here's an identity you didn't need to work out this should be 36 000. oh ben what have you done 193 minus 893 minus 9. you silly sausage so question 18 said here is an identity and that gave me a little pause because i thought the idea of identities which is really important was only really discussed at a level in school and a bit out of date right gcses get to mention it but then i saw the identity and i was like well okay of course it's this one which i know we both feel strongly passionate about everyone should know like it just comes up again and again difference of two squares yeah the way i thought about it was they'd written here as an identity and i assume that must be like code for gcse students of you don't need to prove this or worry about it this is something you can use i think is why they've called it here as an identity i wanted my interpretation i'm interested in the fact they did use the three line equals sign which again i've used i've talked to a-level students but i've never i don't remember teaching to gcse students when i was a teacher but hey it's good notation and actually i'd be glad that gcse students know what that some things are always true and other things are equations which are sometimes true like which you can solve yeah yeah anyway um i have a bad feeling about this question and my marks you may you did lose a mark here yeah this is your second drop mark what did i do uh you made a slight error so you you split it up into the 193 and the seven and obviously you do 193 plus seven multiplied by 193 minus seven but you said that was 184 which you've subtracted nine 186 isn't it what was i thinking so something about it i think it's a classic it's just a classic calculation slip isn't it it's an awkward one right when you're subtracting you know what i do minus seven it's a tricky one but well this i i can now see kind of i can i'm looking at my script and i'm now remembering the slight mental process i was like right it's a three you take away a seven i know three and a four couldn't even make seven so it's a four but it should have been forward less yeah yeah i then did the calculation correct but i wouldn't have got any credit for that so i guess i got m one a zero for that is that yeah yeah yeah yeah because i think the first line you wrote out one nine three plus 7 multiplied by 103 minus 7 that was the method mark yeah so and then it's just and this was a must show you're working one so actually even if they got the answer correct they wouldn't have got any marks is that right i've been looking at the marxism now three thousand seven hundred sorry thirty seven thousand two hundred which is the correct answer with correct method not seen scores nothing literally nothing that which is harsh well um i guess they said that's right you're right it is it is the first well not the first one but it's one of the few that we've seen that say you must show you're working so it is clear nice okay so part b he then was back to her yes just spot what was happening which i think for both of us was super easy but i can imagine that being quite tricky people who aren't familiar with the difference of two squares and who who don't feel this spectacular elation that we both feel when we get to use that little trick like it's gonna be easy [Laughter] question 19 was like a one marker again this is uh it's a b mark in the market scheme and b stands for book i think originally it stands for like a thing you've learned from the book um yeah so you can just write it down but i feel like if you've spent any time working with fractions and decimals this is like well of course it's a knife and i know this one yeah that's what i thought but then i think i also actually wrote a little bit of working but then realized that it was one of those questions when you didn't have to show any working but yeah i started scribbling on there as well but i can't remember we both like added working completely unnecessarily because as you said we both immediately knew it was a ninth just because we're used to working with decimals before we leave question 19 um i do need to show you what i wrote on this because you did a little bit of extra work uh nice proof hey so i thought i did it yeah yeah you did the proof you did the classic letter x equals thing uh do some multiplication uh do some hand wavy about infinite decimals expansion which clearly line up and you can subtract which you can but i think needs some justification uh but you never do the justification gcse uh and then i i like it i like your smiley face uh end of proof symbol as well that's that's a pleasing moment for me good good there's a couple more of those i think i got you can tell this is the point of the exam where i'm kind of i don't know whether i'm losing it or what but i'm like starting to draw i can do this unfortunately the next question was a proof question wasn't it okay uh question 20 the one i didn't like i bet ben's gonna smash this now isn't he well we'll see i i am guaranteeing that there will know his circle theorems before i've looked at this i think he will know his circle appearance let's see as i didn't still don't probably should look those up this one so i'm gonna just immediately and again i say this in the video i do not know my circle theorems so i was just so lost on this i spent like five minutes in the video just being like i can't remember my circle theorems yeah i just cannot remember that like that's what i meant about something that you learned for gcse a level i can't remember and i've never used it ever again i'm not saying it's useless but it's just not something that's ever come up for me being an actual mathematician and i think this question particularly uses one of the circle theorems that is traditionally the hardest one for the kids to remember gcse and the one i've used least often going forward yeah i know you wrote down all the names and everything like this is why i want like i want you to explain this because really i don't so i gave you the marks because as far as i could tell you're using what the exact what the marketing says you should use i will be honest i have no idea what the alternate segment theorem is so the hardest thing about this question as well is that the diagram uh got used for part b as well and i think both of us added to our diagram when we're looking at part b and so the diagram becomes a very unreliable guide of what we were thinking shall i talk through what i did because i think this was the hardest question on the on the exam is that is that yes yes it definitely was for me you know i would love to because as i said i can read your solution and i gave you full marks because it looked similar enough to what was written in the mask with my very like oh yeah i think that's right i'll give him the marks are you seeing the generous examiner that i am i'm gonna draw i'm gonna draw a little bit like your hand-drawn version oh look at that circle i'm dead impressed with my sorry that's never going to happen again i'm pleased with that one there's an a there's a b and i know that the question we might pop the question up on the screen already but um hand drawing a diagram actually i always find really useful so all my comments about you hand drawing stuff i quite do draw a diagram anyway it forces you into thinking doesn't it yeah yeah and i i did i think i watched a tiny clip of you because i was this is where you lost marks right this question yeah yeah um and i watched you thinking about it and there's a tangent here yep and both of us thought long and hard about why that makes 90 degrees with the line to the center because that's a circle theorem that i think we've all used going forward and you remember exactly you see that all the time yeah yeah but not but but this is not the center because the center's not involved in this and even if you put it in there i think you can solve it if you put it in there and did lots of work but hey that's not what they were testing here yeah instantly i think that's how you prove the alternate segment theorem uh which was your only get out clause if you couldn't remember it i didn't know it i didn't know yeah and it was going to be a hard proof to do anyway so let me just catch up with the question the triangle abc is isosceles with ac equals bc so both of us i think put a marker on like that to indicate that um confusingly later on the other side gets involved as well but yeah part a it was just this wasn't it they also told us that cd is a tangent which has made all of us think about right angles but that didn't help so it wants me to prove a b prove a b parallel is that notation okay parallel to dc yep so i got stuck straight away but because of the isosceles triangle i think i immediately labeled these two and i think i probably called them well actually you know i wrote down a reason straight away i said angle a b c is the same as bac uh brackets ice awesome yes and actually i was happy with that this is so far we're in complete agreement this is right yeah and i think i gave no i see i couldn't give you the mark for that even though i know having watched your video oh that is controversial i swear that was the first method mark i swear that was the version okay let me finish the proof and then then we'll dissect why spoiler oh maybe i'll give you one out of four for part a and maybe that was the mark that you got okay uh and i'll show you why but three marks down is the biggest step we've seen in this play anyway so first of all those angles are the same we both know that because i isolated i think i was worth one method mark then uh this is the classic one so the alternate segment theorem i'm going to draw over here says if you've got a tangent uh touching a point on a circle and you draw a chord that touches where the tangent touches then the angle off that chord sort of like z angles right well it's in it's in the other segment so the angle between the segment and the tangent and then the angle in the alternate segment the other side are the same that's what the alternate segment theory and you can see how that's useful here because in this case you realize that that one is the same as that one okay right those two are the same yeah those two are the same so can you see how but then because these two are the same as well we've got that's also the same right that one and that one being the same and that is the z angles although you can't call them z angles and expect to get mark i think right okay in the gcse exam i see so you've written an alternate segment theorem to get the abc angle yeah so we said dca so yeah that one in that one and then you can like from those two lines you get this one uh which is therefore they're called corresponding angles which proves they're parallel and i had a big doubt about whether this is the converse of normally if you've got parallel lines because they're parallel you know the angles yeah where's this thing about the angles i'm like yeah i'm pretty sure there it's an if and only if but i was like do i need to prove that i don't think i do i'm not going to so i think the mark scheme was looking for those three things it was looking for actually let's have a look at it so look at the marks okay ah an alternate segment theorem he's literally wrote alternate seg how do you know this i mean this is fair play ben you've got the mark it's going to the maxi but like alternate segment theorem what is that not happy but anyway well done uh you have the mark it's on the market alternate segment theorem this is nonsense because i read the mark scheme right i read the mark scheme and i still didn't know how to answer the question i don't blame you because i think it doesn't tell you what the alternate segment theorem is they just state it and i have no idea so they're down are you seeing this on the screen now acd equals abc so that is the alternate segment theorem bit i think a cd yeah and then the next line is abc is bac uh that's the isosceles thing and it okay the comments say except both with the same letter on the diagram so if i flick over to your script because you'd labeled them with x that's for my isosceles yeah i could give you that m1 mark i think yeah cool but then i couldn't so i've got an m0 label up here because you didn't reference this angle at all so that's my red marking there yeah yeah yeah i i got lost yep and at that point i think all the method marks are dependent like so this is m1 dependence ah i see you have to have those earlier too exactly get that one and obviously then to get the answer and the accuracy mark is is with m3 awarded so once you've lost one of them the dominoes are all which is what like feels like isn't it but yeah if you don't know the alternate segment there i agree that i cannot get more than one well i think this is a tough question for gcse but i'm i'm again glad that gc has now changed slightly to include rigorous proofs now they always kind of were in there but in practice they weren't tested very hard in the exam and i think this is about as hard as the reasoning for basic circles gets i agree yeah um and given four marks for it is a chunk of the marks on the exam so uh without knowing the circle theorem off the top of your head i i'm not surprised that you ended up losing marks i've still got loads of writing on my face i let's get rid of that but then unfortunately and sorry to break this to you meant part b lost to mark as well yeah i guess i completely guessed because i didn't know exactly uh what was going on so i knew that a b and d c would be parallel and i hope you're impressed with this and equilateral is still technically isosceles yes so therefore everything we've done in part a would also therefore hold so i was like they have to be parallel for that reason and i remember watching your description and i completely guessed between the other two because i was like well i don't know uh so i'm guessing did it rely on the alternate angle theorem again however so you take the top one which is like of course it's still true because you've generalized from the this is now a special case of the first one so but it's the ac bisecting bcd and actually there's a nice comment to make about this so um ac bisects bcd or ac bisects bad so either so is this this line here either bisects that angle that's one of them bad is it or that angle and you just take the wrong one and the only so i was doubting myself as well uh but the i did just check like because this line and this line could have met at a different point they could have met up there and everything in the question would be the same and that means so obviously that other angle would have changed yeah so although it could bisect i'm like that one's not fixed so this must be it and there are other reasons as well but that was the only reason i got to in the end and i feel like that that was using decent geometrical reasoning about like invariant and variant points to get there this is a tough question i lost all i i'd literally lost the will to live on yeah at this point i was like i'm done with question 20. can i please move on well and you and you really get a strong glimpse of what it feels like to be a 16 year old sitting in this exam if you haven't got a nice friendly relationship with things like circle theories or dare i say with maths in general the anger creeps in pretty quick doesn't it yeah why why do i care yeah taking random boxes it put me off i certainly feel like part a um put me off definitely from doing part b i'd had enough i was like right i'm just moving on but it makes you feel better i spent a long time on 20 and i was doubting myself about the proof particularly because i was like i'm using a converse of a theorem i thought i knew and yeah and i had a sense of relief on question 21. i'll be nice i'm nice to my students all right so i'm pretty sure ben knows what he's talking about i still have no idea what the solution to this question is and it's just mentioning names of things that aren't explained but it's in the mark scheme i'll give you the benefit of the doubt ben i'm pretty sure you do know how to do this one well done all right i'll get i'll give it yeah so simultaneous equations right yeah brilliant we'd all have to do those um you got full marks on this by the way yeah yes so you it in or did you yeah you've substituted and i subtracted them i substituted in because yeah they give me the second equation in the form y equals i was like well i'm just just going to use it whereas you rearranged it so that you could sort of subtract the two which is yeah uh a completely equivalent method and actually a lot of gcc students prefer that subtraction method because it does feel like even if you panic that that algorithm of like line them up try and get a coefficient matching and yeah sort of exactly yeah yeah particularly because when you lined them up that the 2x and the negative 2x were like they're going to cancel yeah so actually i think your method got you there quicker um and more smoothly algebraically but i mean that's the point isn't it unless you do lots of practice algebra you sort of fall foul of of the fluke of whether the algebra pans out nicely or not and true yeah if i'd done my method even if it's correct and was less confident in the algebra i think i would have tripped up more easily because i had more fractions to faff with so he's saying that c d c to d is the same game c to a and then a to d yep so i did it right 22 was vectors that was uh i quite like this one i had to think for part b so part a was just about retracing realizing that you can add vectors in any order to get between two points that kind of idea wasn't it and it was just a question of remembering how it works doing the addition and then smiling in relief it's the answer that they had the answer they were getting yeah but part b i had to think about yeah well remember that you needed and you've written your like lander as your proportionality constant way too complicated and i'm i messed that up for a while because i think i'd written lambda on the wrong side which you can still do but it ended up confusing the hell out of it harder yeah yeah yeah yeah that wasn't the wrong side anyway um i nearly nearly knocked your mark off for this really what what how did i nearly lose a mark uh do you can you see what it says in the question there's a bit in bold you must show you're working did i not show my workings well this is just about enough i'm guessing then well you there was a there was a gay jail free card in this one but i would like i was like i completely agree with your reasoning there's part a done one out of one and then you said bc was that by going in that regression and they got you a method mark and then it says we need same ratio of amounts of a and b and i can see your reasoning so k must be four to make that that really should have shown that dividing the two numbers and things yeah there we go loads of chat about this uh they wanted to see the ratios being described for the method mark and then a division so that division was what they were looking for uh to get the second method mark and then four for the accuracy mark but because it was my show you working i was like oh wait how many marks can i give him can i only give him one maybe however if you scroll down through here the mark scheme continues on the next page they clearly had a few issues marking this one for real alternative method alternative myth additional gut another page flipping here we go special case answer four with no working or no incorrect working bull marks and i think that so i wrote on your script that's what the sc stands for i got a special case [Music] so i looked out well but i've improved my exam technique well i don't think you do i don't think you do but you need to improve your gcc exam technique if you're going to take gcse again that's what i mean i feel like a lot of i guess circle theorems aside yeah every other mark i've lost or come close to losing is because not because i haven't done anything wrong sorry not because i've done anything wrong it's because you're working at a different standard of mathematics i think exactly i'm doing it in a different way that isn't in any way this is a really nice discussion point for us to have and for students to have i think because proof questions are not black and white they're no they're human dependent aren't they and so if you're proving something to an academic from oxford i don't know maybe you work with them from time to time you wouldn't go through that division to prove it you'd be like you can see that and they're like yes i saw a half an hour ago stop wasting my time whereas on a gcse paper you do have to show it and that's a really interesting thing for me math is a fundamentally human exercise when it gets important when you're trying to prove stuff and it just means at gcse level the bits you have to demonstrate you've got to go through more steps and i don't think you should go through those steps anymore i'd be worried if you had two in your work [Laughter] that said the exam would lose marks unless there's a special case so i think if when they did this and they were marking lots of works i think they saw lots of good candidates probably do exactly what you did and they were realizing that this is ridiculous we can't penalize good candidates because they clearly understand it they felt that they just didn't need to show that division so they put that special case in and that that's the sign the system is working even if it does occasionally penalize you for these irritating things we have to give a power of 10 2 to the 10 that's what he's got and that was from figuring this other stuff out that looks fine to me that's the answer three marks happy right well the next the next one was fine next one was powers of two this one yeah i think it was how you do it was two to the power ten like unless like silly errors of subtraction were were possible there but neither of us made them which is a relief 24 was just plugging in zero wasn't it for x i did a little sketch remember doing this thinking like originally i was thinking to myself and i'm guessing this is where there might be a mistake for a candidate to make do you just sub in x equals naught or do you want x minus 90 equals naught that's what i was kind of and you know there are some reasons in my head yeah of course i know to plug in x equals not but i did have that moment of thinking about it and i thought oh that's probably the common error that might happen in this question and i think and i tried to solve it in two ways just because i found myself getting in a bit of twist because i drew a sine graph yeah and then you've got one in red and one and one in blue yeah and then haven't you well the red one's the shift right so i could see that i expected the answer to be negative one and i was like let me just justify this because you could i could have done without drawing that i could have realized that when i put 0 in i get negative 90 and so i put that red mark on the left of my script at negative 90. that was the other way like either use the blue graph to think about it or the red graph and either way i was like right it's got to be negative 1. i don't think i've made some stupid mistake but for students actually drawing the graphs i think is way more useful than they think like just having those graphs absolutely understand yeah yeah anything involving signing calls graphs is super helpful i agree oh this question um the gradient of op is equal to two it reckons yes good perpendicular and tangent hey like he did it the same as me and i thought i was doing it wrong get in um with his negatives as well as half perfect now i'm actually happy you got that one right because that's how i did it i didn't think it was the correct method no i was really happy with this one because i thought that i was winging it with my gradient must product of gradients is minus one i was like i don't think that's gcse knowledge don't know how else to do it i'm going with it and then when i saw that that's how you did it i was like yes thank god can i do that yeah we did it almost exactly the same way didn't we yeah and i wrote way too much too many words no so yeah you're right you you form your triangle you know it's forming at a right angle because again circle theorem the one that i know the this is the one we talked about earlier right yeah and i wrote since tangent to circle is perpendicular to radius at point of contact way too much whatever the one useful circle theorem helps you and then it's just the product of the gradients that are at right angles has to be minus one yeah it's interesting that i i think a lot of gcse students know that fact as the perpendicular gradient is a negative reciprocal which i think is a really bad way of remembering it it's much neater to think they multiply to negative one and then you can do whatever you like uh so yeah so i liked your style on that i didn't i didn't write the words i like or style but i do i do like and then um and then the second one i kind of saw this one coming maybe work out the length so that was just kind of a couple of bits of pythagoras theorem oh you had to look at the equation first the equation of the line got to work out the intersection well we have a point on the line and we know the gradient so we can work out its equation and then you can work out the um the pythagoras theorem for the triangle yeah and i think in part a you'd already got a bit carried away on your paper and started yeah and i'd wiggle the radius which i think is useful right you eventually need it oh wait no i'm not sure you do you did because i remember thinking oh am i going to adopt tom or mark's for going down a rabbit hole he didn't need to go down but then later on you found your groove and yes yeah yeah yeah this one took me longer than than um i would have liked to be honest i think about this one well actually i don't know just a little glimpse of your script on screen here like it's really nicely laid out this one because i can sort of follow your thinking and like things are occurring to you uh and then you so you've done all the radius calculations here just because yeah you knew you could and you're like i want to do that all right yeah that was before i figured out that it was going to be the product was -1 things yeah and then you got the equation of the line and i like the little sketch and that that's yeah bull marks i think good good save yeah same for you same for you 26 26 uh the answer should be minus 24. i remember i did this i spotted my own sign mistake on this question i'm really annoyed anyway right 26 i made a sign error i'm so annoyed i noticed this i noticed this when i was marking your script i got the right answer i just forgot the minus this is the classic slip like negative signs errors happen to the best of us don't they and it just you just moved from one side of the equation to other and forgot the negative that's it i don't think much to say although if i was your teacher and i was going to give advice the same advice you've given to me before i sound too patronizing which is like check your work right but one yeah the best way of doing that in this case is to have a diagram because it's obvious then that the the intercept is negative and you would have noticed within microseconds that is that it's way too high so you didn't differentiate this is how i did it because of course at gcse you wouldn't technically know how to differentiate even though it's a perfectly valid method you better have given me the points for differentiation ben because it's it's correct maths just saying ben i guess has done it the correct gcse way i'm assuming you didn't penalize me for differentiating no no no no definitely not it's a good message i said this in the video i was like i know this isn't how a gcse student would do it but i'm just going to do it because i've had enough at this point it's a good point i forgot to pick up on that because you're using a level method i mean sledgehammer to crack a nut i think is a technical phrase for it isn't it yeah if you couldn't differentiate how would you do it do you would you have a way uh i've now spotted how you do it's the shift isn't it so plus b moves x squared up by b and plus a inside the squared moves it to the left by and it's nice that that's also the completed square format so it's a it's now a big thing in gcse to recognize the completed square format contains yes information about a vertex the turning point and i i it's a really lovely piece of algebra that i love teaching at gcse but a lot of students just it just passes them by and if they have done differentiation there's nothing wrong with that technique so i was really glad to see that sledgehammer getting brought up yeah okay good interestingly uh at this point uh i finished my paper i i packed up i was like i was thanking the camera i was like i'm done 50 minutes or something clearly 26 and i think my script i was because i was working on the actual paper on a pdf it just wasn't loading very quick because it's just loads of graphics or something so i scrolled down i was like oh it's all blank i finished and then five minutes later i was like whoops there's question 27 so on the screen you could have lost you could have possibly lost another three i did and it's on the recording so i'm not going to take them off you because you would have still won so it's it's you know well so let's talk about that technique is a lot better this one took me a lot longer than um i felt it should i was talking through what you did um well for me i was like trying to figure out what sine of 60 and tan of 30 by drawing graphs of sine and cos and then obviously for tan calculating sine of 30 over cos of 30. yeah so i just drew the graphs and then just because but i'm guessing good gcse students would know 30 60 45 40. exactly and that's a relatively recent upgrade in the last few years they've explicitly said whereas before a level students were expected to know 30 60 45s because they're super useful right they turn up all over the place yeah yeah yeah they have they have put that in gcse now and i think it's a a common uh discussion point that only higher students really need to know this like if they're doing the foundation tier they wouldn't bother teaching it um which is sad because actually they are really useful but it's worth sharing one thing um that i remember being really pleased about is that when you can't remember what they are all you have to do is draw a triangle like equilateral triangle it happens to be helpful if you draw the twos and then because it's equilateral you get a 60 and you get a 30 and then pythagoras i think gets that as to be a root three i think it was an a level exams when i was doing a levels i remember drawing these triangles in margins to make sure i'd remember the angles right and then sine 30 is one over two straight away and the only other one you need is the 45 degree one so if you do one one root two then you get the 45 degree ones for free and so i i'm often thinking of those and by now they're kind of internalized and i think of them in my head but i mean i kind of did the same but i did the graph and then figured out you know um because for example it's that nice point there cos of 30 has to be the big number because i know there's like root three in there and i know there's like a root two and i know that i know roughly what the numbers are yeah you just gotta remember which round they go flat at the top and then decreases faster you know that cos of 30 is the root three over two one and then from there i could kind of figure out stuff but it's an example of a gcse question which was harder for you than it would be for a gcse student who has learned the things that they're ready to use but you nailed it you got full marks and i hope i did two 60 degrees oh yeah you did it it mattered that they said it was a cute because if you were trying to solve cos x equals a half there were some other answers to fine yeah yeah so yeah yeah yeah although i don't know i think just that you circled that and you also wrote 300 but then you only for your answer wrote 60 because i guess you'd making sure you had all the cases at that point i noticed that they'd said acute for a reason i was like i'm going to try and get bonus marks to be honest at this point i was just relieved i'd remembered that this question existed which is why i've circled end of questions and like oh thank god i noticed that finally that is a very very good 78 out of 80. well done ben i'm pretty sure you beat me because i couldn't do that circle theorem question and i know i got another one wrong so i'm i reckon i've got about 75 or 76 and ben's got 78 there's no way i've beaten 78 so i'm already now going to accept graciously my defeat very well done ben i will i'm clapping you as you can tell i'm really excited that you beat me so well done well done so yeah that's that's it we made it to the end now did we add them up correctly did i think so no i i'm just i'm just thinking of what what i dropped so i dropped the feathering mark yes for the graph i dropped the mark for something else that was a silly mistake that was a gcse so feathering on question 10 yeah or the double line then there was a single mark on the not simplifying fully the four overs yeah of course four six being two thirds yeah that's fine yeah and again like it's all right it's a marketing circle no other shame should be attached it's just one of those things that mathematicians do uh the that was two marks down so then you lost four marks on question 20. i thought at least you thought i was gonna lose all five on that one luckily you remembered what i saw these triangles were and you've got some credit for it and then the sign error i'm not i'm not two i'm not i'm is that right four five six that's seven marks that is right isn't it yeah yes and your two were the the um which one the approximation of the prism you forgot the oh yeah something you did like a muddled calculation and then um the subtraction you subtracted nine instead of seven on the difference of two squares i think both of us are fine so the one lesson well me apart from circle theorems right if you take out me not knowing circle theorems we were basically identical yeah because that was four marks right you'd have got 77 though and like we it was just little slips there was a sign there a simplification error and a controversial feathering area yeah which i'm inclined to ignore to be honest if we cut that graph stitching out if you've done it on the paper that wouldn't have happened i think i probably would have still feathered it i didn't realize i honestly just as i said it's a habit i have yeah when i draw a graph i always do it several times like in you know any of my other youtube videos when i'm drawing graphs i do it like that so i think to make the shape look right yeah i i think i still would have done it interesting you didn't do it on the cumulative frequency but i know whatever however it pans out we're now seeing what they penalize and what they're rewarding at gcse and nothing as which is much to my religion nothing that we did i think is sort of in direct contradiction to what the gcse exam scripts wanted the students to do which is good i think the main takeaway if i could sum it up i think the main takeaway is neither of us really did any wrong maths or agreed a minimal amount of incorrect maths what's interesting is that i did wrong calculation right so i didn't do wrong math i did wrong calculation and i feel like in my head that's different calculation apologies yeah none of us did apart from me not knowing circle theorems none of us did any wrong maths yeah some calculations areas uh calculation errors correcting which happens to everybody they're all over my a-level exams as well so i knew it was going to happen it's the pressure of recording what you're doing um which is the same as a pressure walk through doing an exam as well right i mean the pressure's real and it will be true for everyone doing the exam but it's nice to know that the uh the examiner's notes recognize all those things and they're award marks where they can and so it's exams are pretty fair and they have to be that black and white in their mark schemes in order to make it consistent that's the and it's frustrating when you get a special case and you're like but actually from my experience i did one season of actually marking papers for gcc and a level i was going to ask about this because i could tell you knew how to mark exams it was well over 10 years ago so don't assume i know anything but it is it was a sobering experience because actually the main combat you have as an examiner is boredom like you're marking again and again but every script you're looking at is really matters to one person like yeah so you're getting bored in that guy whatever zero marks it's not okay and like that pressure really really starts to play on you which is why i'm really glad the examiners reports they're really full they're even more full than what we used to market because yeah they have meetings all the time special cases get handed to a team leader and then taking up the chain if they need to it's done well but actually i think both of us have been reminded now what a maybe a difficult job to do it well is oh god yeah and they rely on people teachers volunteering around the country they're not they're not volunteering they're getting paid but um this is like an army of teachers who are busy people saying i'm also gonna mark some exam scripts and thank goodness they do we are we are very very very appreciative of the efforts from all teachers in everything they do well genuinely either you know hopefully they know this from us but like yeah we we love teachers and everything that they do so the conclusion of our not a competition is that we both did fine and uh that's a good outcome i love how this is coming from the person who won the knot competition it's fine we're gonna do a rematch we're gonna i don't know what it's gonna be yet but we are absolutely i'm saying it now right it's like all these boxing fights that are whitening at the moment you know that contract that you signed beforehand saying that the loser is allowed to invoke a rematch clause the the rematch clause is being invoked and we have a rematch on unknown competition is that what you're trying to invoke yeah yeah yeah i mean every video title we published about this said this is not a competition uh but i am up for doing something like it again whether it's another gcc another a level or something like i'm just going to float it out there like the uk mt uk maths trust challenge things that would scare me it'd be quite fun they would be terrified yeah it's like puzzle thinking more at the same time we'll figure something out but no um thank you so much ben for for joining in my ridiculousness of doing exams it's been it's been really good fun it's been great to have somebody else to share the experience with and uh yeah i really appreciate all your insights in particular with the marking because as i said i even with the mark scheme wasn't sure exactly how it all works so it was really nice to hear your input onto how as someone who's much more familiar with marking and gcses like you know to know how to actually interpret that and and to give us those insights into how they actually check these things as long as you don't take my word as gospel because there's plenty of times i'm making it up as well but yeah and it's been really nice to have someone like even if you mark your own script like i know what i was thinking and so watching someone else a good mathematician do it trying to get in their head is a very good experience to remind myself what market feels like so thanks thanks for including me you're welcome i've learned a lot i hope everyone watching has learnt a lot please do remember to subscribe to my channel if you've enjoyed this video check out ben's channel which is sparks maths um you'll see if you haven't already you can watch him do the whole paper now that you know how he did you can see how it should have been done if you happen to have only watched mine um and you'll hopefully see both of us around on some more number foul videos uh very soon as well so again thank you everyone for watching and i'll see you all soon thanks bye you

Channel: Tom Rocks Maths

Views: 86,821

Keywords: gcse maths exam, gcse maths higher, higher maths, higher maths exam, high school math exam, oxford professor, oxford math professor, oxford university, oxford maths, oxford mathematician, sparks maths, ben sparks, numberphile, numberphile presenter, tom crawford, tom rocks maths, tomrocksmaths, sparksmaths, school maths exam, gcse maths, gcse maths walkthrough, gcse maths exam walkthrough, how to do gcse maths, learn gcse maths, tom rocks oxford, tom crawford exam, oxford

Id: 4DCb5P_uknY

Length: 83min 43sec (5023 seconds)

Published: Sat Oct 23 2021