Hi evhow. You day great. Excellent. Well, I heard you got a conditional offer from tombridge school, so that's terrific. Very welcome on that. That's great news. So that means while we're kind of dipping into fun beyond gcse stuff, starting the a level, we also need to be thinking about you getting that nine. So the agency sent me the paper you did recently and asked for us to go through it today. So can you get that paper up? That's. Let me see very. So this is let me see what year this is 2018. That sounds about right here we go. Sorry, could I get it? Yes, absolutely. Go get it. I will sunback you got your paper with you then? Yeah. But could we just move on with the calculus and just correct this paper though? Like just correct it and let me know my mistakes? I'd like to go through together partly so I can tell you sort of as I'm thinking also, I'm not paid for marketing. King, time to be really prapaoh. I will try and mark it as quickly as I can so we don't spend too long on this and then we can go out to a level. The first thing that does caught my attention. So question one, no problems there. Question two, I notice no working ings and it is a one marker. So I just want to check you definitely or understanding that, talk me through why one is five. Because it's a. Because they are both boards of because o and n or omr obviously perpendicular to the. Are midpoints, so they perpendicular to the two chords, and those chords meet at a point p, so they, so they must be a tangent. They must be two tangents to a smaller circle called radius of five. Okay, Yeah that's a maybe a slightly indirect way of thinking about it. I would be thinking more about the right angle triangle and the fact that od and oa are both radii. I'd say it's a more direct wait, but Yep, that's correct. Nice. Okay, next up. Yeah, I'm sorry this will not be the most interesting lesson, but important to do it. I also noticed no workings on question three, so just talk me through that. I'll give you permissions for the board. I use calcufor that. Yep, very enough. I mean, I feel you be able to do that. Doesn't say no calculator. So fair enough. Can you show me how to do that without a calculator? I think that's perfectly fair game for a non calculated paper. Zero, one, two, five is one over eight. And so one over eight. To the negative to so it's to the two power and then to the root of three foot. So the power of two of it is 64 over one. I'll be around square root and cubit maybe slightly quicker. But Yeah, excellent. Question four, that's fine as well. Let me just check your workings here. Yep. Question five, that's great. I should probably ask first of all, are there any questions that you know you found after I think make ly see multiplication because I just searched it up and then because I haven't done it that often, but I could do more past papers on it. And which topic was that through? Uniform? Uniforms? I know. Not. Sorry. Not uniform matrices. Sorry, matrices. Oh, this time. Yes. This syllabus. Oh, we should definitely look at that. That's not usually in gcbut. This is ci, okay, well, let's make sure we get to that but we can just that's also this on that list for sorry I say I'm not hearing you very clearly today so that again also list list okay, okay. Well we'll come to them one by one. Let me just check this. Yep, six that's fine. When you say lists, do you mean like question seven? Okay. So let me see if you got it right and then if there are any issues. Yep. So you've got that right that the first one. So the intersection is things that are in both lists. So integers six up to eleven, that's ten. Absolutely. So this is slightly non standard notation for part b. I'm guessing they mean. Not that's not very standard notation though. I'll look up what your syllabus wants for that for part b, that's not a standard set notation. So I'll look up there's lots of notations for this, but Yeah so don't worry about part b because that's not a very normal notation. Didn't part a make sense? No, it made sense, but I just think I lack practice on it. Okay, well, you've done it perfectly well there, but I'll I'll make a note of that more set fair practice and I will go have a think about b. That's not a normal notation. Okay, question eight, that's looking good to me. Yep, perfect. Lions in Africa. Yep, that's quite right. I assume you plugged into a calculator, right? But that looks good to me. Yep, exponential decreasing. Clearly you'll find the nearest hundreds. Yep, no problems there. Okay, midpoint. So there's some scrubbing. Oubut, the answer is looking good to me. Are you happy with ten? Yeah. So you could tell me what the general formula is for the midpoint of two points then. X one plus x two over two, y one plus y two over two Yeah averaging the coordinates absolutely okay. Upper nerbounds. Yep. Okay, times three, Yeah, very good, no problems there. Excuse use. Very good. You've done the 180 minus, right? Let me just let me just get a calculation. Check your workings there once. Second. Okay. Yeah. P very nice. So we've clocked that we've got an arithmetic sequence here for 13. Let's just do a sense check. N equals one. Yeah gives us minus four. Excellent. Very good. Shaingly unwanted Ted, okay, first thing I noticed with question 14, boring thing, but but important looking at that, I'm not super clear on what you mean to be shaded and what you mean to be not shaded. So just be super clear and neat with that kind of thing. But that's good. Grinto yeup probably because of the photo taking, because I did it with pencil. Yeah, quite possibly. But Yeah, just be careful with that for my Yep, I'm happy with that. Very good. And good job getting it the right way around matrices gcc. Now that's a new one by me. Interesting, but you've done a correctly very good. If I haven't done the international boards in a while, you definitely wouldn't get this in netexcel. Okay. So have you learned how to find the inverse of a matx, a matrix? Because this looks to me like maybe just looked at I just looked at it. So like one over ad minus bc and to the matrix, like we be a. Yeah so basically there's just a formula. It looks like you might have done it from scratch. Yeah because I didn't know the formula yet and I just researched it. Excellent. I'm just saying whether you've got it right, because I think your dad wants this marked. So well, show me how youused the formula. Let's worked it out together and see if you worked it out from scratch correctly. I think probably not. So let's have a go at this question now. Nice. So I can see you're clear on that. It is basically just learner formula, very good. Okay. So question 16, I'm seeing some scrubbing out. Yeah, I didn't get it. Okay, let's have a look at this now. Let me just see whether you've got any Marks there. No, I think probably not. Okay. So looking at it now, if you have any fresh ideas how you might approach it. No, okay, what if I sort of rephrase this as what they're saying is that the left hand side is the same expression as the right hand side. If I were being picky, I would say they should have put an identity sign, not an equals. If I were being picky on the exam board. It is a slightly poorly worded question because Yeah, I would say there should be an identity sign in the riddle. Does that change? I'd view it. How would you approach it in this case? Clsay that negative twelve x plus a equals. And I say that absolutely. You can say that we're doing the same thing to both sides. So that's fair game. Yeah. But there's something that might be more of a natural thing to do if we're treating this as identity. We're saying that the left hand side and the right hand side are two different ways of writing the same thing. Then there's another technique we might consider matching them. Sort of what exactly do you mean by that? Two bx matches to negative? Yeah. So I'd call that comparing coefficients. But Yeah, absolutely. Excellent. And then can you finish it off? Wait, not route. Yeah that's we don't minus six for b don't we? 来也。Yeah that's looking at me so slightly misleading. If I'm being picky, there should be an identity there because it doesn't really make sense as an equals statement. So I'll cut some slack there. Nicely done. Okay. But in terms of looking forwards, if there is a slight little non clarity on your exam paper, just seeing that it doesn't make sense as an equation. So I'm going to treat that as a an identity I think is a good takeaway. Okay, 17. So you found the gradient excellent, and you flipped it. Excellent. Excellent. Plugged in your numbers. Yes, I'm happy with that. Very good. Excellent. We've been doing quite a lot that lately. Okay, let's look at this pie chart. I can't see from the scan, have they given you the divisions or did you have to draw them on? No. They said there's 120 students and and the number of students for University training at work. So have they given you how much of the pie chart did they give you? Did they give you the the line, the circle, the circle and then the starting line? Okay. Nice to the presumably just looking for the proximate one then Yeah, the main thing is having University as just under a half. Yep, I'm happy with that. Nice. Okay, we have a panther bone. Oh yes, straight. So the construction things are really just things to memorize. So if you haven't leart them, then that's fine. But by six bcd. I mean, that looks like a bisect to me and it's a memorizing thing. So if you're happy with that, then I'm happy with that. Happy with that Yeah Yeah Yeah I mean bsectors and the construction structions it's there's only a few I think Yeah it's just a learning thing and it looks right so I'm gonna to Yeah with that right 3 cm from e. Again, that's just a construction. I'll take that as fine, less than 3 cm nearer to dc. Then to. Bc one on that side of the line. Everything. Yes, I think that must be it's quite a strange question really. Couldn't they've been doing angles? But. Yeah, I'm happy with that. Okay making it subject the formula look. Minus six. Well, without even checking it, I reckon you could do it in about half as many lines. So here is a challenge to you. Do it again. Let's see how few lines we can use. Let's get some efficient maths going. Sorry, which question are question 20? I'd like you to see how few lines you could do with it. Not convinced what you did is correct. Let's see what we come up with. Okay. Can you double check the second line for me here? Be happy with that. Yeah technically correct. Not necessarily the most direct way of doing it, but correct now. But I mean, I don't know the most efficient way doing it. Well, I find this is something that's hard to teach in a sort of set list of rules. I think you've got to feel for it. Some general guiding principles is I'd always try to undo fractions first. Fractions are kind of tricky and nasty. So a first step for me would always be to undo fractions. Because that's a lot easier. Now can you see a really direct way from here? Wait. Now have a think about that last step and have a think about whether that was a sensible mood, if it's not incorrect, but think about what the question is asking. So some general principles for you. I like to get rid of fractions, and we want to look at what we want to be the subject, and we want to get all terms with that letter together. So what do you mean? I get all terms of that together. So here we want to make m this subject. So I want to get every term that has an m in it together. So I'm seeing two m's on opposite side. So I'm wanting to remedy that absolutely. And then my third guiding principle is I want m to appear just once, because if we want it to eventually be the subject, we need it to just occur once. So what technique can we use so that we only write the letter m once? Yeah and then can you see the final step? Yeah Yeah, that looks better to me. So as much as this isn't particularly interesting, it does just need practice, I'm afraid, because there's no set of rules. It's kind of just a matter of functioning fluently in a language. And it is a skill you need to move forwith your math. So a bit boring, but I'm afraid this does just need practice. So maybe I'll just like start every lesson with one so we can get it out the way. I think that will make sense. Yeah. Yeah. And are you clear on the general lessons that would allow you to reproduce this next time? Okay, cool, let's move on. Then question 21. Yep. Yep, that's. I mean, I can't see what's shaded on it, but. What's meant to be shaded on question 21? Is it just the photocopy that's dodgy? You see if I show it to you here. Oh, yes, I can see that. Great. Thanks. So you've worked out the sector perfectly. Excellent. And yaagria half A B sign c is the way to do that. Can you see the little slip you've made? You've got the right method. Little slip that I think you wouldn't have made if youwritten more down. So that's the lesson there. Can you spot it? So you've written a half ab sign c, which is great. That's exactly the technique I would use. Unfortunately, then you've gone straight to an answer. Now writing things down is really helpful. It helps us catch these little mistakes. I to be fair, maybe there's not a mistake there, but I definitely think you should have written more down, though. Let me just check. Sorry, I was doing it in my head. Same issue in an exam. Write stuff down because it's so easy to make slips. If not, but I buy because I wrote it in the calculator in just one line. So yes, the advantage of writing on the paper, if you have made a little slip, the examiner can give you credit for method if you've written it down. So I'm a big believer in writing stuff down, but that's correct. Let's move on to 22. So we're doing between ab in the horizontal. Yep, okay. So I like your calculation, but I reckon that ac worked out not ab. Do you agree? So go for 21. This is on 22 now. I'm happy with your calculation though, but I think you mean ac. Yeah Yeah, I meant to c great. And then I'm happy with the method. I'm not going to check all your plugging in, but just to be just make sure you've got strategies to avoid little slips because they happen to us all prime factors. Yep, nice. And I like that method. Very happy with that. So I think it might be correct. But just to check, you understand the idea it tame through your method for 23b. So finds. Will start with one and then start with one of the numbers, find its prime factors and see if there's anything. And then find the other numbers, prime factors, see if there's anything it doesn't have and then times it by that. What do you mean by it doesn't have show me what you did for this question. Show me your full workings because again, you haven't really written enough down show the working because the prime factor of 56 is two to a third Yeah time 73. Two is two times three times seven. It definitely contains two contains seven but it doesn't contain three. So if I multiply that by three and then by seven, it should get me the loit's common multiple. Okay, just to sort of first some ideas days. And so we're not doing anything I wrote. What we're really doing then is we're doing the for each prime factor, we're taking the maximum from the two, aren't we? Yeah, Yeah. So that's a kind of nice general idea we can apply there. Excellent. I'm happy with third 24 cumutive frequencies and all right. Median you've done 25 now I can't see many workings which might just be the photocopy so taught me through your method for these so I can check but you're happy with because it gave me a graph so I don't even need the working well I would find myself drawing on the graph but I probably can't see that so just talk me through your methods. Yeah there are more excited did but Yeah, that's what I thought probably happened properly. Well, as a refresher, explain to me the method for finding those things. The median is the cuthe half of the cumuated frequency. So 40, which maps to 25. Yeah nice. And how do you do the cortiles by the a fourth and a quarter and two quarters of the accumulated frequency and then find the range of that and talk me through how you did see. So anything further than 40. So no, I mean like accumulate the frequency that maps to 40 minutes and then 80 subtracted by that. Excellent. Very nice. That all looks very happy, right? 25. Yep, the first one's correct. Very nice. Inverse. Yeah, next. Okay. Can you spot the little slip in part two? Yeah, it's supposed to be x minus two over five. Yeah. Can you see where the error slipped in? Yeah, I changed right to other, I mean, I should have made a negative five x, yes, or I would do it the other way around. Yeah, make two, two or 2s side. Yeah, through the other side. I think while it is not very interesting, I realithat I think just your fluency with the basic algebra is something that maybe might be holding you back a little bit just relative to how strong you are on all the other topics. I'd say maybe just a little practice on the basics there could be quite good. Okay, puppy. All this fun. Yep, Yep, very nice, excellent. I will just calculator check these ones. Yeah p nothing wrong with that. So why is it just is this in two different parts? Because it's gone back to question one now is this now non calculator or something? No, it's just another part and we didn't bother printing the first page. Okay. And is this still calculator? Yeah, Yeah, it's definitely so calculated. Okay to I Yep, very happy with that. I mean, all of the paper to our calculator. So okay. Yep, nice percent excellent. I mean, I really can't see how youget these wrong. If you have a calculati'm sure they're right. Wait, I think I wrote six a wrong. No, I changed it back, I think, okay, let's check. Nine. Nice. Yep, nice. Six, a thought. Well, it's a bit a little unclear. You're in the risk of it being read. It's the roll number 5000207. Yeah you've written the right thing on the left, but then you've scrubbed to zero when you've written it in the box. Do you see? Yeah. So I mean, I can see that you've written it right once, so just be super careful there. Standard form. Yep, very nice. Okay, simplification. This might just be a reading thing, but have a look at a seven for me. Yeah. Can you spot what's wrong with seven? There's okay there's two cues so I think you've treated them all as the same letter, which might just be the Pand Q's looks in there Yeah so just a little too sig Fig okay, explain to me your understanding of significant figures. How does it differ from decimal places? The first zero after the floating point counts, and if there's nothing before the floating point, it doesn't count. But that again, that's not how I would conceptualize it. But first say that again. It counts from the first non zero digit or starts from the floating point. What do you mean by the floating point? Dot. From the decimal point, you mean? Yeah, Yeah, Yeah, okay. My sort of way of doing significant figures is you start from the first non zero digit. So I'm not quite sure what you mean by. Including the point, I've always done significant figures as being the number of figures that aren't zero. So I would do 76 and then four is rounding down. So I'm not quite sure what you mean on that. The floating zero. Unless this is an example specific thing, I don't know, I'll ask. Let me just. Yeah no, I think I'm a little bit complicating as so I had Yeah so significant figures are the figures basically that aren't zerthe complicating factor is that if we have zeros inside it, so to speak, they count. But in this case, so you know it's it's 0.076Yep. But are you happy? Why Yeah are you happy that this is not a significant figure because we haven't got to the non zero numbers yet? Yeah, but I don't know why I'd learned it somewhere that did counts or something. I think what you're confusing is if we had something like. What's that to three significant figures? 0.0701. Yeah I think that might be what you're thinking of. When we have zeros kind of inside, then they're significant. But zeros all to the left or all to the right counts as not significant. Yeah. Yeah happy with that. That's just a little tweak I've been thinking of that that sounds fine. Thing g Yeah so you've you've managed b well, which is harder actually because you've got kind of confusing zeros. But Yeah, that's correct. So you've managed the hard one. Cool. Let me just see your without calculator work. Yep, nice. All right, Yep, no problems there. And the subjects yeyou've done that rearrangement really nicely at eleven. Very good. Last, please. That's fine. Please check that. Quite a strange one at twelve. So we don't need rounds to half centimeters, but let's just have a little think about that one. Nothing big. Stairs. So the way I would double check this in my head is I would be working out values. So 42.46, for example, what does that round two to the nearest half a centimeter cent squared, 42.5. Yes. Starting myself now. That's surrounded to near 0.5 cm. So it has to be the number that follows it. Yes, it's just it's weird because we're not doing to a whole like a decimal point. It's kind of odd. Let me just Yeah double check that later. So I'm having a senior moment, but I'm sure right, let's have a look at 13 writing this as a fraction. Excellent. You're doing this this technique. So 100? Yep. Absolutely. Ten. Yep. So I'm going to take them off. Yeah, very nice. Excellent. And for 14, I didn't think of the word, but now, Yeah. So it's a reflection around the line. Y equals x reflection in the line. White. Yeah, it's reflection. Okay. Let me just sort of mark this when we can think about that. So yes, a very good idea to think about what happens to one zero and zero one. So again, I would like to see more working. So I'd be doing. See what happens to one zero. Zero one absolutely. I mean, it doesn't have to be multiplied, right? You can just tell that the matrices it's you can just tell from these two values though. Yeah or that I mean, you can just multiply it as a general principle, but. That way you can do it with any vector. Yes. So if one zero is going to zero one, Yeah the x and y zero one, Yeah. Well, you could be extra sure of that. Just sort of throw some more ideas at you is we could do it to a general vector. Yeah. So I assume if you're doing matrices, you've been taught how to do the multiplication. Yeah. So we've got y and x. So Yeah, we're just flipping it. So you're quite right. Reflection in X Y, if you're in the exam and you've basically done the matths, you just can't think what the words are. The more you write down, the more the examiner could think, Oh, I see where they were going. I'll give them all but one of the Marks. But good stuff there. That's advanced stuff for gcc that's not in most of the syllauses. So very well done. Okay, let's be distance. In time. So if we want in meters, then we should be there's two unit conversions from hour to second and kilometer to meters. Yeso, again, I would love to see a lot more written down to avoid little slips, but let me just check. That's fine. So to meet. And. Yeah divide 16. So Yeah 180 times 20 just check your thumand seeing some slightly again, I think writing a lot more down would help you just go through your sum again. Now show me exactly what your thinking is. Sorry, I lost track of which question again. 15. 108 times a thousand is one zero eight. And that divided by okay, nice. It's correct right? Yeah that I'll just check when it have been a slip, but I think that's fine. Okay bit algebra. Yep, good. Yep, very nice. That's good to see your exponent laws with your brackets are going well. Good progress there. Nine, six. Yep. Very good, the direct proportionality, right? 18, let's see how directly you can do this algebra. Nice. I don't know which theyprefer, it's kind of a matter of taste, but I would leave it factorized on the bottom. So I wouldn't reexpand it, but theyhave to be very mean to document Marks for that, okay? Just. She. Yeah. P nice, excellent. Yep. Very good. Quadratic seven oc minus b Yep b squared. -48. Space? Yep. Yep, absolutely. Kind of we'll assume you can plug things into calculators. That's really good though. Okay, speed time graphs. Yeah, absolutely a is absolutely correct. But just to throw another idea out there, what feature of a speed time graph represents the acceleration? Yeah. So we could also just work out the gradient. I mean, I just remember that formula. So Yep, no, I'm just throwing different ideas at e. Yeah minus. Oh. He minus 1012. Talk me through the first line you've written down with it. B, I think there might be a large issue there. The first line of b don't me through that equation you've written down. The equation of I don't know, I forgot the word, the shape is called with I think it's. What can you explain to me the first thing you've written down the top plus the have the bottom the top times the plus the base times the height and then divided by, Oh, you've done the whole piece. Yeah, Yeah, I'm in the parallel. So half. T plus t minus ten Yeah okay. Yes, I guess we could not work. Yes, I guess that's it is a kind of trivial trapesium. Yep, absolutely. And just to emphasize that the property you're using there is that the area represents that I'm just gonna I'll do at that literally. I'll just check later that those sums come out all and there's something a bit dodgy looking to me but that looks good. Okay, 22 is simplifying. So two x squayep on six plus right? Yep, good factorizing on top. Yep, that was good to me. Very nice. Okay, try and get prison aand that Yeah so this is much the same as before. Very good. I know Shimi probably wanted me to work out pp or something. So wait, say that again. No, no, nothing had thought had wanted me to work out pb and then ap. So I mean, I think the way you've done it is is spot on. I like that. Working out ac, absolutely. And then using ac and pc of tan, that's exactly how I would be doing it. Very nice. Okay. 24, 26. Excellent. Yep, good matrix stuff. And then matrix multiplication is always a bit fiddly, isn't it? Three minus one? Let's just go through this because it is it's super fiddly. I think there might be a slip there. If only need to check your understanding of quite a tricky topic. Talk me through what you did here, and I'll see if there's any issue. So three times one is three, two times two is four. And what why two times two? What's the sum you're doing there? Here, here and here. Yeah, that's not quite right. So let me just let's go through this. So you can learn a formula, but the way I do it is like this. This goes with this to give here. Yeah. So isn't it the same if you swap the two matrices? No, no, no, no. An interesting feature of matrix multiplication is it's not commutative. So with numbers, a times b is the same as b times a, not the same with matrices. It's an interesting feature. And then I'll just go through them that times that gives you that one. I kind of think of it as a little kind of almost like a dance kind of thing rather than a formula that goes with that to give you that one. And that goes with that to give you that one. So I kind of think of it as a how to illustrate this online. It's kind of that with that, that with that, that with that, that with that is not a very good way of explaining it. I guess if we did a formula, let's do a one day, two, a, three, two, four times, actually, that's and it's going to need to make that smaller. So we do a one, B1 plus a two, B3. Then we do. Over here, a one, B2. A two, b four. Down here we do a four, B3. A three. So it is basically just a really complicated formula. I'm trying to think how to communicate this over zoom, but I think of it as the patterns. So maybe if I just talked with you how I would do this multiplication to show you how I'd apply that in theory, because I wouldn't be thinking about a formula so that if three, one, two. So I'd be thinking this with this, so three times, one plus one times minus one, three minus one, two. Then going along to the right, I'd be thinking this with this. So 32, 14, so ten. Then for down here, it's this with this. So 21, three are minus two, minus one. And for down here it's this one with this one. So 34, twelve, 22, four, 14. I'd not really thought about how I would communicate that as an idea. It's quite fiddly. It gets easier with practice because you kind of just learn the kind of motions of it. So have a look at your textbook, see how they've communicated that, and just a bit of practice. But the main thing is to be aware it's absolutely not symmetric. We can't swap them, which is kind of an interesting feature of matrix multiplication. We're bit out of time. I will finish going through that and I'll send that back to you and your parents. Sorry for a bit of a boring lesson, but we got to get that nine get you into tommbridge. But well done again on getting that conditional offer. Great stuff. Thank you. Great bye and see you next time. Bye.