GCSE Maths Tuition Lesson 23 the HARDEST GEOMETRY QUESTIONS

uh so I found a bunch of like new style of questions from Hello ma how are you from kind of older papers that you might not have seen before so this is technically old spec but it's all the same maths but it's different styles of question which I thought could be quite useful for you um I do remember the kind of topics you asked me for hey Evie how are you um but I figured we'd do some kind of different style of questions to try and like you know throw you off course a little bit because you guys are pretty strong yeah I'm doing pretty well I'm doing pretty well I had a bunch of classes canceled on me um which might sound bad but it means I have to rest dying maths Mark so soon I know I'm sure you guys are going to do fine you'll be fine and even if you aren't at least then you'll know which topics you struggle with and you can practice those so either way it's a good thing 100 not too shabby not too shabby still scared you'll be fine actually there is something I wanted to talk to you guys about um the kind of maths department at my school put together a few predictive papers as well so I could actually do a few of those on stream too so that could be quite interesting um the style of question is kind of weird which might be a good thing might throw you off a little bit but for today we've took a bunch of kind of different styles of questions um and again I got these from Fairly old past papers which I'm I'm fairly certain you haven't gone back to like 2013 before uh so it's kind of interesting they're from a slightly again the maths all stays the same but it kind of throws you off a little bit you mock is next Wednesday okay best of luck best of luck okay so let's get started so we have Point P has coordinates five seven and we have Point m is 1 2.5 m is the midpoint of the line p q so Q is going to be somewhere let's say down here and all we need to do is work out the coordinates there are two ways to do it one way is kind of using the actual formula for the midpoint which is the fact that you add the two x coordinates together so X1 plus X2 and divide it by two and then you also do the same thing here however there is a slightly in my opinion easier way all you have to do is if you look at the x coordinates for the midpoint and point P there's a difference of four which means there should also be a difference of four from this one can you take P from M yeah that's exactly what I'm doing so if you look at X it goes from one to five that's a difference of four so I'll write that down just make it slightly easier so all we're going to do is for Q you'd also have to add 4 to the x value so the x coordinate is definitely subtract 4 from 1 which is negative 3. okay so we have to do that is subtract four a difference of four yeah so the reason why it'll also be a difference of four is because the midpoint right is directly between p and Q right which means it should have the same distance between each other so what that means is if you add 4 to the x coordinate you'd have to add 4 to the x coordinate from Q as well the other way to do this by the way is you can also make like a big triangle and you know that the distance will be the same but that's a bit a bit more complicated yeah no worries um with the Y value we can do the exact same so what do we add to 2.5 to get seven uh it's 4.5 so we're going to do is subtract 4.5 which would be negative two yeah negative 2. nice and easy and that's the coordinates for Q two more questions yeah starting off relatively okay but there's a question later on I think might be interesting Circle theorem question this one I also thought was quite interesting is a non-calculated question so the circle shows a circle inside a square ABCD is a square of say 10 centimeters so all these sides are 10 centimeters work up the total area of the Shaded regions in terms of Pi so when you look at this you might think straight away that the Shaded region is just going to be the square subtract the circle and you'd be 100 correct that's exactly what you need to do so the square is quite easy right since all the sides are 10 centimeters then we can just do 10 times 10 and that'd be it now what about the area of the circle though that that bit was slightly trickier I'm wondering if anyone's uh seen that yet um again it's not it's not like super difficult but it might be tricky to see so if you have a look 25 Pi is correct radius of 5 10 is the diameter well done so 10 is the whole width of the circle so the radius would be five so all of you are correct so you're just subtracting pi r squared so pi times 5 squared so what you're doing is doing 100 minus 25 pi and we can't simplify that any further so that is the answer nice and quick three more question not too bad box plots so I find that the statistics side of your gcsc is generally neglected by your schools so this might be slightly trickier for you so we have a box plot gives information about the wages of a group of 16 year old workers and 18 year old workers if you'd like me to quickly go through what a box plot is then let me know um but yeah with the compare the distribution you get okay never mind I didn't actually write it out you get basically you need to do two points okay when you compare distributions the two things you're comparing is the spread this is where you get your marks and average good good good okay but you're getting you're both correct yeah so you need to compare the spread and yes into quartile range well done okay so with the spread some students uh use the range the range is not the best measure of spread okay the interquartile range is better because it's taken into account like 75 of the values which is a lot better so yeah you're going to be comparing the interquartile range and in this case the median and this will give you three marks always but you can do it in as few steps as humanly possible so the interquartile range you need to calculate it in fact this was four marks because you need to work at the IQR so we need to read it off so again this is the lower quartile that's the upper quartile so the range is um the problem with the range is it takes into account extreme values right so with the range I look at this value and this value the problem is if you look at how far away this range is that's a big difference in this box plot here that's 75 of the values right oh sorry yeah the interquartile range takes into account um 75 of the values right because this is the bottom 25 this is the top 75 percent fair enough um so the the upper quartile takes into account three quarters right and this is one quarter I see what you mean actually yeah what I what I meant to say is that it goes up to three quarters of the values but you're right if you subtract them they'd be um 50 of the values but the idea yeah it is 25 I see what you mean now um I think I worded that wrong the interquartering system's about 50 of the values but the interquartile range is uh three quarters yeah you're correct tv perfect so yeah all you need to do is work out the interquartile range so for me that's quite easy so I think it goes up in 205 so 5 10 15 20. yeah so it goes up in fives so this would be 210 subtract that'll be 130. which is 80 pounds and the interquarter range for these dudes over here is 280 minus 210. which is 70. so yeah the 16 year old workers have a larger spread of data so you would just write 16 year olds and the 18 year olds have a higher average which in this case is the median uh is this the salary no wage okay okay so yeah all you have to do is compare the spread so the interquartile range and the median so the reason why the interquartile range is better is that it doesn't take into account extreme values so if you look here the actual the higher values are quite far away from the majority of the data so it might not be an outlier per se but it's not really fair for one person's earning 300 like was that 380 pounds whereas most people are earning around this amount of money so that's why the interquartile range is better generally speaking now it says here there are 200 workers who are 16 years old work out an estimate for the number of these workers whose wage is 130 pounds or more so I'm just going to write 200 people and if you look at 130 that is actually let me get rid of this quickly that is this value here so if you notice that's the lower quartile so how would I work out the number like an estimate for the number of people who earn above 130 pounds for this you just need to know what the lower quartile represents but I'm interested to see if any of you know quarter of 200 I see why you got that I see why you think that it's not you're on the right lines but not quite so remember it's more than that so how many people earn more I know how but can't type yeah it's kind of hard to type it out so yeah for none of these workers who's weighted 130 pounds or more so as ma said this lower quartile represents a quarter of the people so a quarter of the people earn below 130 pounds so three quarters earn above 130 pounds so all you're going to do is do three quarters of 200. so one quarter of 200 is 50s Times by three is 150 people does that make sense because that was a bit a bit wonky 0.25 times Y is 200. good okay this next question the reason why I was quite excited when I saw it oh yeah you are close Mark you probably would have got one mark not not two he's 25 about yeah perfect with this next question I haven't seen it in a while which makes me wonder if they're gonna bring back this style of circle theorem question this year maybe potentially but uh I do think it's a relatively interesting question have any of you seen something like this before to be honest if you've done a question that looks like this you'll know exactly how to do it which is cheating I'm drinking but don't say right how it is I'll give you a little bit of time to have a think about what you would do it's a bit tricky I'm not gonna lie it's a five mark question by the way five marks so expect to do three steps because again you need to give a reason for each stage of your working out so you get some marks for the reason remember if you don't give reasons they will just give you zero even if you get the right answer so bear in mind that I'll give you a little bit of time is anyone completely lost if you are that's completely fine because this is a tricky question I think I have an idea of what to do here I was in a segment interesting you can use angles in segment potentially then you make an angle subtended interesting I'm not saying nothing I'm not saying anything do you draw a triangle from the line do you mean from I'm not saying anything Evie I'm not saying anything I'm not doing anything what'd you mean by that Ma do you mean from P to o or from like Peter r or entity I mean I have to give some in from the point O draw a line straight down isn't that already a line straight down as in from o to to where or is it not on one of the points I think I finally found a question that you guys are struggling with finally all it took was going back to 2012. 11 years ago from o to p OSP is OS 48 yeah I mean it gives you that finds the O from 180 and then double it to make the new system I'm liking this oh ah interesting it's an interesting move Lila interesting move I'm not giving anything away because I think Evie will uh rip my head off so I'm just going to stay quiet for a little bit I want to say that you guys are doing very intelligent things even if they aren't right they're intelligent things and I like that have a think about what cycle themes you can see already foreign from o to m you could you could I would find it with a piece honestly you probably would yeah oh I'm not gonna lie if you had it in front of you it might be a bit easier a 90 degree angle interesting oh okay I think I can see where you're coming from I think one of you said alternate segment theorem that's interesting potentially get you somewhere I feel like I need to start writing soon mother is something you could definitely do start RSP equals SPM uh uh knock okay ma you're correct that is one way to do it so I actually would have done it a slightly different way all right I'm gonna do it this is the way I did right but two of you said alternate segment theorem and that actually makes a lot more sense so you can see that this line OS is a radius and this is a tangent so they would overall meet at 90 degrees so then if you do 90 minus 48 you do get 42 degrees and Alternate segment theorem would say that this would then have to be 42 degrees as well that was clever I actually did it or I would have done it in a slightly different way so when I looked at this question just now what I was looking at is if I draw a line from o to P which is what I thought you meant initially Ma yeah exactly you can get that these these uh lengths are the same because they're also the radius which means this angle here is also 48 degrees because remember the base angles in a triangle and Associates triangle is the same I thought that's what you meant that's why I was like from where from o to r o to S but oh yeah that makes sense um damn you guys did not bad and then you just work out what this angle is which would be um 84 degrees and then angle subtended at the center are twice at the radius so you'd also get 42 degrees both of which are completely fine so I was happy with that you also know that this side has to be 90 degrees right but we're only looking for this angle here so what I would have done is I would have drawn another line from o to m which that's kind of bad but what it does is it it cuts this angle in half so this angle here is 21 this angle is also 21 so then all you're doing is doing 90 minus 21 to get your final answer of 69 degrees so either way you did it you would have got that so I should probably write out the reasonings because this is a bit messy right yeah either way would have been fine I did I did hope that so I'm thinking that they might actually do something like this this year this this year I think um oops also actually there's a question I wanted to ask you guys um which example are you doing for English you can I no I mean I would if I could but yeah AQA okay AQA oh I might have a present for you guys basically I I have this structure I'm your English tutor well you say that I have a um a year 11 student on Wednesdays and uh basically we went through a kind of structure for the language paper one and paper two and she managed to get very high on her mock grades so I might share that in like a video or something yeah you haven't been taught Circle theorems Jesus Christ all right you need to check your spec by the way because there's probably quite a lot they haven't told you so there's some statistic stuff I'm willing to bet they haven't done um just yeah the amount of many talent to walk and I say but yeah I might do it in like a video or something I don't even talk like everything yeah that sucks that royally sucks oh well yeah okay it's a good thing okay so what I'll do then is I don't know if I do it as a live stream Maybe they're nerfing you they are they need to hold you back they can't get you that 100 you know identify do this as like a live lesson or I just record it as like a video but either one I actually have uh I have I have structures for basically um question one through five for paper one and paper two and the student did pretty well and she said it was because of the structure I don't know but either way I'll um make that video am I good at English I think I'm okay I think I'm pretty good at it English literature is harder for me because I there are so many different books they can give you um that the ones I studied at school and the ones I like tutored might not be the same ones as you guys like there's so many different ones like Of Mice and Men and in and and Inspector Calls I'm fine with um Macbeth is okay as well but that's something that's mutually exclusive I don't know man I read a lot of books so I don't know if that helped me with English or something like the quality of your English is a big part of like GCC English shockingly I know the rest of his memory and I'm quite good at memory oh man Lord of the Flies yeah see I haven't actually even read the book Lord of the Flies so I might have to I'd have to read that if I wanted to try and teach you it I love literature it's just that there's so many different books they can give you it's a bit tricky to keep up with it you will not revise it oh come on Evie you can't just focus on what you're good at really if you want to fall asleep I feel like no that's Heart of Darkness something that I've never learned yeah well until I get your nine exactly so what I can do then the thing is English language that's Universal that's the same for everyone pretty much so I could upload some stuff on English language too literature you might be on your own on that one not gonna lie I I don't know if I'll be able to I don't know how many books I can read I could probably share resources and stuff but other than that okay uh honestly given how quickly you guys got the circle one I think this four marker might be a bit of a softball for you might be a bit easy but uh oh conned by someone on Tick Tock for English language help oh did you pay like a tutor or something you need to do this one I'm assuming you mean the maths one right do this one okay um yeah the English video I'll make one I'll make two or two technically you bought a structure people pay for them oh okay well the one I want to give you is going to be free so don't worry about that I'll go through it in the video to like to do it properly okay that's good I actually kind of got a Creator's block recently where I wasn't sure what kind of videos to make so that's given me a bit of hope I can make some English language videos in the meantime I'll make one for paper one and one for paper two and if it's useful and I won't charge you for it Okay so with this one if you ever see do physics videos I should definitely get on that's actually a really good point I feel like this is like my lesson instead of your lesson at this point okay anyways um physics Is My Jam I love physics so much oh anyways so whenever you see these two parallel lines like this you should be thinking of Zed F and C angles but bear in mind you can't call them that in the exam so although I'm saying z f and c angles never call them that in the exam they're called alternate angles corresponding angles and co-interior angles respectively make sure you refer to them by their proper names so if I look here can you see that D to e to A to B looks like a big Z right so whenever you're unsure of what to do in these kinds of questions just start working out angles but I can quite easily say that this is 54 degrees and again what I'd write is 54 degrees because alternate angles and yeah I probably should have capitalized it but you know whatever YOLO right okay the next one is one that doesn't really come up that often but basically if you make an X with two straight lines then they're opposite angles are actually equal to each other like this okay and what this is called is vertically opposite angles so you might not have seen it doesn't really come up that often but it is technically on your spec which again is why I think they might try and throw at you this year now you might be thinking vertically opposite but it's also the horizontal ones I know the naming sucks but yeah so can you see here this is just made this x kind of shape is made up of the same two lines so that means this angle here is 70 degrees because of vertically opposite angles again so so far you would get you would get two marks right for working at this angle in this angle and a reason okay so now I can work out this angle right and that would be my third Mark why because angles in a triangle add up to 180 so this one here is just 180 minus 70 minus let me know if I'm going too quickly by the way there's a bit of a delay on the chat so I can't actually tell when you guys want me to stop and talk so 108 minus 70 is 110. minus 50 would be 160 so that would be 156. I'm an idiot did I really say 156 56 degrees all right okay 56 degrees not 156. cool and then for the final Mark all you have to do is say that X is equal to 180 minus 56. which is 124 because angles on a straight line add up to 180. so if you don't give a reason for any part of that working out you drop the mark okay so even if you're right you drop it so again this is just angles on a straight line so angles in the triangle angles on a straight line vertically opposite alternate angles it's a lot of writing but it is four marks so I guess it's kind of expected go any questions about that at all perfect good perfect yeah his x 124 yeah X is 124. now hello Ali how are you but I hope that that was okay so yeah four marks is bit beefy but when it does say um give a reason for each stage of you working a common question I get is do I have to the answer is yes every single stage you need to give a justification for it which is unfortunate but you know now this one yeah this one looked fun it's a full marker which I did subject Evie you're on it there we are not bad so the first thing you want to do is work out the total interior angles so what I mean by this is this is what the angles in a shape add up to and the formula is n minus 2 times 180 where n is the number of sides how many sides are in a pentagon five five minus two three times 180 540 degrees good I'm glad this formula so with this formula whenever I ask students like in schools or in tuition they they don't recognize it and they say they've never seen it now of course some of the time they've just forgotten but sometimes they've just never taught it this comes in clutch sometimes not always it's not the thing is so with like the GCSE and everything since there's so much content your school's not going to finish all of it so the bits that don't come up that much they skip but this is a four mark question which you can't do without this it's impossible so yeah so because it's a regular shape exactly it's a god formula only thing to teach at all well there you go at least I did something right if it's regular it means all of the sides and angles are the same so each one of these angles here are going to be 540 divided by five which is 108 degrees if you're wondering how I did that I just divided it by 10 and then doubled it divided by 10 is 54 double is 108. um I can't remember if this was a calculator paper or not so I'm just going to assume it isn't uh yep so now here's going to be the interesting thing right this overall angle is 108 degrees this tiny part inside here oh is going to be half that anyone unsure why actually I didn't explain it this is a line of symmetry which means it should bisect the angles that it goes through just like it bisects the sides it goes through that's why the inside bits 54. just for anyone that was wondering okay now this angle here is 90 degrees why because when you draw a line of sorry a line of symmetry any angles it goes through it bisects so it cuts them in half any size it goes through it's um it bisects does it have to be symmetrical to assume that yes because it the only reason why okay I'll ask answer Evie's questions first so the reason why I can do this is because they tell me it's a line of best it's a line of symmetry that's why I know it cuts it in half that's why I know it has to be symmetrical if these weren't lines of symmetry I wouldn't be able to do that and mods one two question Evie already did it means to cut something in half the only way you can cut something in half is at a 90 degree angle so they're perpendicular bisectors perpendicular meter 90 degrees bisect to Cotton two or to cut in half that's a really good question so if it looks like a line of symmetry can you assume unfortunately in maths just because something looks like it's something you you can't assume it no never assume if they don't tell you or it's like implied because of circle theorems or something like that you can't assume how'd you get the right angle good question so with a line of God I keep calling a line of best fit with a line of symmetry any sides it goes through it's going to perpendicularly bisect so it's going to meet at 90 degrees that's why it has to cut in half which means it meets at 90 degrees 108 over 2 as it says straight line yeah if it's a circle with them then yeah you can because it will tell you like um radii and tangents meet at 90 degrees so they might not show you it's 90 degrees but they'll tell you it's a tangent and you can see if it's a radius that's what I mean by using Circle theorems but in general you can't assume things because of this thing up here diagram not accurately drawn which means even if they draw it looking like a 90 degree or looking like it's symmetrical doesn't mean it is so they have to tell you basically absolutely I can well I can try to anyway Okay the reason why I'm doing all this by the way is when I first looked at this question I didn't know what to do if I'm making a confession so I've started working out stuff and from there I can see what I need to do now I'm going to work out this angle here and that angle let's just call it X oh no don't call it X let's call it y is the third angle in a triangle so I'm going to 180 God minus 90. minus 54. 180 minus 90 is 90 minus 54 is 36 degrees now the reason why I worked that out is because of the vertically opposite angles so if you look this is an X shape made from two straight lines hello bucket yeah yeah yeah you're getting it correct then what I need to do is I know that this angle up here is going to be the exact same as X so what I can do is I can do 360 minus 36 and yeah hello bucket how are you minus 36 again it's a minus 72 which would be 188 right yes uh so bucket what we're doing is I've actually collected a bunch of different questions that were quite tricky so I'm going through just a selection of different questions so it's not actually a specific paper if that makes sense well 180 minus one much less effort that is very true Evie oh yeah because angle's on a straight line yeah you're right that's actually easier and then divide by two um which is 94 degrees which is our answer no he's bucket I have an eyes yeah oh apparently I don't hopefully that makes sense it's a four mark question um a bit involved what Evie said is actually easier so if you look it's just a straight line so you could just do you know angles on Australian add up to 180 that's a very good point any questions at all so I thought this was a fairly unique question in my opinion you know fairly different so it's always worth going through okay um unique in a bad way uh yeah in a bad way uh Lila uh yeah I'd say so what if you it's been a couple of months since I've taught chemistry to be honest um because I don't really have any science peoples anymore but I used to be able to do them very well yeah hmm I don't know I think I can explain things decently well I don't think I'm like smarter than anyone or anything else like that though okay yeah next question then this one is another interesting one I thought so it's a it's a humble four marker uh just like we've known for the past while you have to work out with x's doesn't seem too tricky right some kind of glitch in The Matrix uh these are higher questions bucket although there is a bit of overlap this question specifically is definitely a higher question sohcahtoa interesting well done bucket damn well done bucket not bad at all um so yeah you're 100 correct well done I thought I'd take a bit longer so evil sorry Lila you're correct sohcahtoa and then you can use uh you're going to use sohcahtoa in order to find out what the angle is but as bucket pointed out we need to know one other side in order to work out an angle using trig so we can use the sine rule wait oh okay I think I see what you mean oh I see yeah that works as well Evie yeah so you could use it as like yeah not quite Pythagoras bucket but that was a valiant effort the intended solution is to use the sign rule all right the intended Solutions is assignable but Evie's pointed something out which is fairly interesting you could make this one big right angle triangle and use trig to work out what this angle is and subtract 30. yeah although it wouldn't be 17.6 it'd be 10.4 plus 5.2 which is 15.2 15.6 yeah there are two ways to do this then yeah so the way that Evie's talking about is if you make it one big triangle to it's a 10.4 plus 5.2 which is 15.6 this is very clever and 18. so what you can do is work out this angle and then just subtract 30 from it to get X which is 100 valid 100 valid how do you even do sine rule for this where's the angle you need for DC um what you would do yeah I mean that might take a bit more so the way I the reason why I said um sign rule is I'd use the sign rule to work out this angle and this angle would just be 180 minus that angle and then we can just work out X from there right oh yeah Mark I can do that absolutely we'll finish in a second um ev's way is probably the easiest so there's the sign rule there are two ways you can work out this length and then do that but that takes a bit longer I was going to work out this angle work out this angle just doing 180 minus it then just doing 180 minus 19 minus that angle but you know uh I'll bow my head I think this is the easier way to do it you are you're actually doing a much better job than I am so since it's O and H we're going to use so so we're going to use sine y equals opposite 15.6 over 18. put you in the face cam oh man I should do that actually I just have a screenshot like your name and just shove you in the bottom right instead uh I do have this is obviously a calculator question because it's trig um all that so inverse sine uh 15.6 of 18. that's 60 point blah blah blah and then if we X is just going to be whatever that is minus 30. it's actually kind of interesting though it's basically the same number but yeah 30.1 degrees let's make it your dream is a maths question about you interesting uh okay and how many more questions did I get I think I got way too many questions by the way easy Edexcel math paper relatable very relatable how many questions how many more did I get oh God all right yeah I may have gotten a few too many um considering we only have okay we have we have 20 minutes that's fine let's go a bit faster so I'm not marking this here now not as far as I'm aware reverse cosine rule the problem with that Lila is you need to have a third side yeah so this is the angle we want to work out you can call it X or whatever the hell you want to call it they've given me that the area is 18. so what we can use is we can use area equals a half a b sine C A and B are just the two sides that make up whatever your angle C is so we can work out what the angle is from there and we can use that to work out the other one water's here nice so 18 equals half seven times eight sine C I want to simplify this a little bit before we continue so that'd be half times eight which is four times seven which is 28 . don't know why that took me a bit of time but you know so C is just going to be the inverse sign 18 over 28. so let's just change this [Music] oh okay that is so this thing here is just I just call it the area formula where does the half go yeah why is it inverse sound okay I skipped a step so the half I actually just worked out what a half times seven times eight is EV so a half times eight is four four times seven is Twenty Eight in terms of why is it inverse sine if I continue from over here I divide both sides by 28 and then to get rid of the sign I just did inverse sine is to find the angle yeah well done bucket so yeah that's where I got that from 7 times 8 is 28 yeah no worries I probably shouldn't skip steps that is pretty much just 40 degrees exactly so I'm just going to leave it as 40 degrees okay and what we can do from there is I'm going to use the sign rule to work out X but before I do that I need to work out either this side or this angle this angle is much easier because otherwise I have to use the cosine rule and I'm okay with that no thank you so 180 oh I'm an idiot never mind I can't do that I have to do I have to do the other way so we have two sides we have an angle I just want to make sure I know what we have God yeah so we can use the yeah the cosigner yeah God all right so the cosine rule is we're going to label this a b and c and this is capital a so a squared equals B squared plus c squared this is a very involved question I'm hoping I haven't done something uh too tedious okay oh boy all right why did I pick angle a b c to be science uh yeah um okay so I'll answer Mars question first I didn't the reason why I chose this to be angle C is because the formula at half a b sine C you have to use two sides and the angle between them so the only sides we have are seven and eight so it has to be this angle here a bucket to answer your your question um they haven't actually told as far as I'm aware they haven't told us that you're getting a formula sheet in general but it is normally at the beginning of the um uh exam paper so but they they specifically told us a couple months ago that they tried to remind us that you don't have to get a formula sheet in the exam and they made the point very very clear okay oh perfect mark thank you yeah okay good never mind then you get it on the formula sheet um but yeah they made it earlier how did you label the sides a b and c okay so the way I labeled the sides is I with the cosine rule the side that I want is always lowercase a always that means the angle has to be capital a has to be B and C it doesn't matter which way around you put it I could have just moved them around and it would be the same thing right because you're only adding and timesing them so the order doesn't matter the only ones that matter are a no problem otherwise you have to memorize all the different versions and screw that you don't need to you never need to okay so we have 7 squared plus a squared gonna be so much harder to use a calculator on a keyboard uh cos 40 at the click pause 27 and then okay I'll write that out quickly but then we're just taking the square root because we don't want the side squared of course 5.22 so it wants it to three significant figures I'm going to leave it to 5.22 yeah my phone if I rotate the calculator it just gives me a scientific one yeah like if I open my phone to the calculator I can turn it to the right and I can do like sine calls square roots Etc which is which is Handy yeah um okay damn this question oh it's six marks whoops that makes sense that makes sense so you would get two marks for this first bit two marks for the second bit and you get two monks for the last bit the last bit is you'd have to use the sign rule so in terms of the sine rule again it doesn't really matter which way you label it the only thing that matters is that capital A is opposite lowercase a capital B is low is opposite lowercase b and so on other than that it doesn't matter okay um oh dear God I just okay that's five point two two okay so we can use we can call it whatever we want right so if you want I'll keep the labeling that this is a which means this is a the other side it doesn't matter I'm gonna call it B and B right well this is technically going to be X so what that will look like I'm gonna move this down a bit and I'm going to do the new working out up there because I don't want to confuse you guys the sign rule just says that depending on what you're working out that is extremely specific Lila but yeah uh we'll have to do it next probably next lesson but I'll write that down I'll add it to the list of questions June 2019 paper three AQA oh question 27 that would help yeah Okay cool so in this case we have sine 40 over 5.22 right because a is 40 that is 5.22 I'll have time to understanding uh somewhat small yeah um B is sorry and then sine X God I'm losing my marbles okay over eight right it's for those two so if I times both sides by eight I'm going to get sine X equals 8 sine 40 over 5.22 and then all I do is I inverse sine both sides and then when you see it to three significant figures okay so inverse sine that okay I'm in degrees not good and that would be 80.1 to three significant figures that is a six mile question not bad pretty chunky question not gonna lie but honestly this is kind of the perfect question because in terms of advanced trick use everything use the area of a triangle formula use the cosine rule formula and use the sinewal formula that's literally all of advanced trig so that's actually like the perfect grade six question to be honest yeah that's what I was thinking when I was going through I was like there's no way this is a format question and then yeah six marks makes a lot of sense actually a lot of sense okay we'll do one more question then we would take the questions from you guys oh it looks like I really cropped this badly whoops well you know I always aim to impress damn it okay so I know honestly okay this question is full marks okay that's a bit more human so again if you have two parallel lines like this you're always thinking of z f and c angles but again never ever ever call them z f or C angles ever never call on that you call them alternate corresponding and co-interia otherwise you'll get no marks Okay so FBC is 70 good so as bucket said yeah as bucket said this is going to be a z angle BFC it's yep well done very good he was doing it faster than I can interesting that's actually not the way I was going to do it I was going to do it this way fair enough yeah both these are isosceles 70 degrees well done not bad at all if anyone didn't keep up with that so again you need to do the reasonings right so the first thing you do is you would say um FBC or CBF whatever whatever you want to call it is 70 degrees reason alternate angles are equal okay why is this 70 degrees why is BFC 70 degrees base angles of an isosceles triangle are equal