IGCSE Mathematics LIVE Lesson - Past Paper Questions (Variation & Similarity)

Ajouté : 2026-05-07

[00:00:00]a network problem, just go check on the live videos on um not my Instagram but on the YouTube channel and the Facebook channel.

[00:00:16]Are you ready? Do you have your pen and your paper? So remember, I want you to for those who have not submitted, please um here is your final chance to submit to make sure you have marks. So please, please, please to those who have not submitted, listen closely.

[00:00:32]I'm saying what you're going to do is you're going to write with me right now and you're going to submit as corrections. Can you hear me?

[00:00:46]Yes. Seth, are you in class?

[00:00:56]Okay. Uh for those who need the link, you tell me so that I send the link um the link for submission. Okay, I'll check I'll check attendance at the end of the lesson. Um and then I'll be able to follow those who didn't. Right, let's get started. This is the first assignment. So I'm just going to be moving fast. We have we have four assignments. So we are doing the assignment solutions together. So let's see and let's see how you're supposed to do it perfectly to make sure you going to get 100%. So I'm going to do it for all your assignments.

[00:01:28]If you stop seeing my screen, please make sure you tell me. Right. Right. So this is assignment number one that we are doing solutions for which you should submit is variation and selection. We're going to be doing past paper questions that I did. I'll put another one. Uh maybe I don't know. I'll think about it. Variation and selection.

[00:01:49]So no not variation and selection.

[00:01:51]Sorry, just variation formats. Okay. We are not doing biology. I I'm getting cuz I wanted to teach you that in biology but it's fine. We are doing variation and that's the topic we're doing right now. Now remember what you must know.

[00:02:04]Here's what you must know. You'll get it better as we go along. What you must know is that if they say something varies as let's say they say y varies as x or is directly proportional to x or whatever what you do is you're going to convert it to an expression. If you're given as a sentence the first step is to convert to an expression like this y varies as x this is how you write it. Okay. Then if they say y varies inversely, if you see the word inversely, this is what you do.

[00:02:38]If you see the word inversely, if they say y varies inversely as x, you say y is proportional to 1 /x. If they say y varies inversely uh as x^2 that means it will be y is proportional to 1 / x^2. If it's inverse, then it's going to be 1 / that's going to be the step number one. Then step number two will be to remove this fish and you're going to put an equal sign. When you put an equal sign after removing this, you put a k on the right hand side. So this becomes kx. Same thing you do here. You remove this, you put an equal sign, you put a k on the right hand side. But if it was a fraction like this, the k will now go and multiply the top. So it will be k over x^2.

[00:03:25]It's the same thing. Okay? Have you seen it? Then we can start to solve. Then what we will now do is we will always need to find this K. We will need to find this K. When we have found it, we can answer any question that we have been given. So here it is. Remember this question is coming in your exam probably in paper two or in paper four or both in paper two and in paper four. Are we together everybody?

[00:03:55]Are we together? So here is going to be the first one. Y is inversely proportional. So they've given you as a sentence in the first one. So that you are going to read y is inversely proportional to x + 2 o^2. So you have to write that you have to convert it.

[00:04:11]Let me make sure that YouTube is not cutting.

[00:04:17]All right. Good.

[00:04:24]Here you have to listen now what you do here. You have to make it you have to change this sentence into into the first form. We said inversely proportional.

[00:04:35]Once you see the word inverse, you say y is going to be proportional to one over whatever they will say here. So they said y is inversely proportional which means you say y then you put your fish facing the left. Don't change. If you have a habit of changing things then you're not doing well. You don't change.

[00:04:53]These rules are not to be changed. So you're going to say y is proportional to 1 / what they say x + 2 ^ 2. So you now say x + 2 all 2. This is the first step.

[00:05:07]If you don't have this step then you're not going to get anything. So this is y is inversely proportional to x + 2 ^ 2.

[00:05:15]Then now you change this. This becomes y is equal to what did we say the next step is? You remove this fish. You now put a k. k over x + 2 all^ 2. Well done.

[00:05:29]Then now look at what they say. They'll give you y and they'll give you x at some point to use to find k. So you're going to come here and you say let y be equal to what did they say? 8. Then x be equal to what did they say? 3.5. x be equal to 3.5. You write it like this.

[00:05:47]Now you're going to say where is why we are putting eight. So we put 8 is equal to k over where there is x we're putting 3.5. So it's 3.5 + 2 all^ 2 all 2. And what we want is the k. So we take this to the other side. 8 now multiplies 3.5 + 2 all 2 and it will give you k. 3.5 + 2 is 5.5. So x now multiplies 5.5 all 2 and you get k. Put it in the calculator.

[00:06:15]You could have even put it into the calculator earlier. So you now say 8 now multiplies 5.5 all squared and you get 242 being okay. Are we together?

[00:06:33]Is it it?

[00:06:36]Make sure it's the one. Let's see. This was 3.5 and here x is 3.5.

[00:06:43]Have you seen it?

[00:06:46]Then now you get your 242. Are you seeing students?

[00:06:53]Okay, good. So here now we go on. We're going to now say y you rewrite say y is = k over instead of k you can now put 242 over x + 2 all^ 2. Then now you have this as your first thing.

[00:07:17]What are they now saying?

[00:07:19]W is proportional to X. Another thing we do the same thing again. W is proportional to X. This is what we are now doing now. W is proportional to X.

[00:07:28]Then what are they saying? When you have written W is proportional to X. They didn't say inversely. So you just put your fish facing the left and you put your X. Which means now when you remove this and put an equal sign, it will be W is equal to KX. Right? Now this is another K. It's a K2. So now what you're going to do is what are you going to do?

[00:07:46]They said find Y in terms of W. Look at what you're now doing. Since you're saying W is equal to K2X, you can now make X the subject again. Then you come and feed it here. So let's make X the subject. You say here since W is equal to K, let's put this K. Find this K.

[00:08:04]That's the next step we always want to do. We want to remove this K. K is not supposed to be there. You use this one where you are given both information w and x. So you come and you say let w be equal to 15 and let x be equal to 90.

[00:08:20]You're going to have 90 is equal to k2 by 5. No w is 15. Okay. 15 is equal to k2 by 90 cuz the x is the one which is 90.

[00:08:34]So now you take 90 to the other side. 15 over 90 is equal to k2. What is 15 over 90? You get 1 / 6 is equal to k2. So now you can write and say w is equal to instead of k2 you now say 1 / 6 * x which means w is equal to x over 6.

[00:08:56]Okay? Cuz it just multiplies the top.

[00:08:58]It's a whole number. So it just multiplies the top which is 1. It becomes x / 6. You take six to the other side. You now have 6 w is equal to x. So now we have 6 w being equal to x. We just come and we put it here. So you're now going to say y is = 242 /x + 2 all^2. Now you say let x be = 6 w. Let x be = 6 w. You now get y is = 242 over 6 w + 2 all^ 2.

[00:09:32]And now you have y in terms of w. Have you seen this?

[00:09:45]There we go. So, 242 over 6 W + 2 O².

[00:09:55]Those who don't have this assignment, could you please make sure you are writing these corrections? Yes. Did someone call my name? Yes.

[00:10:08]The the what?

[00:10:12]The where did I get it?

[00:10:22]K2. I got it from this here to say W is 15 when X is 90. So let w be 15 x be 90. Do you understand? From this second statement here, w is proportional to x. So I came I wrote w is proportional to x. Then I have to remove this proportional sign.

[00:10:47]Pardon?

[00:10:53]Yes, it's the second K. The K's are not the same. You don't use the first one and the second. Yes. Each relationship has its own K.

[00:11:02]You understand?

[00:11:03]Okay, that was the question. Yes, each relationship should have its own K. Well done. Good question. Just to make sure.

[00:11:11]Okay, Simon, I'mma give you right. Let's go on next step. This is this one. This is easy. I know. Let's move fast. Okay, let's quickly do the solutions. We need to quickly finish them cuz we don't want to make this harder than it is. We have the fish already. Come on now, students. They didn't even give you the relationship.

[00:11:45]They gave you the fish already. You know the steps. Listen, you are a mathematician so you don't break steps.

[00:11:51]May that day never find you where you throw away all this and you start doing your own methods in questions. That's the deadliest thing. Steps are to be followed no matter what comes. Come rain, come sunshine, come thunder. So you know that for this topic, it's this easy. That's how we make sure we always get things correct guys. That's how we get our 100%. So here we have the fish already. Y is proportional to the inverse. So this means y is inversely proportional to x whatever this root.

[00:12:24]Now we know that when we have this we remove and we put the k. So y is equal to without reading anything. You don't read this. Remove the fish and put an equal sign. Okay? Remove the fish. Put an equal sign. But you then need to put a k. And this will be the square root of x + one. The root of x + one. Now what do we have now? y will be then equal to what? You now once you have it in this form then you can use this information you've been given. You now say let x be equal to 8 and y = 3 which means now wherever there is y we are putting three. Wherever there's x we're putting eight. So you're now going to say 3 is equal to k over because there's one thing we hate and that's k. K always has to go. He has to go this guy. So it's going to be the square root now of where there is x we are putting eight. Be careful there. 8 + 1. This now becomes 3 is equal to k over the<unk> of 9. Uh 3 will be equal to k over the square root of 9 is 3. You take it to the other side. 3x 3 is equal to k. 9 is equal to k. So you can write now to say in this form the equation. But now you know what k is. So you now say y is equal to instead of k you now put 9 over the<unk> of x + 1. Okay. Square root of x + 1. We say to you, well done.

[00:13:49]Well done. You are very good at it. Now the next step you do, next step you do is you now come here. You now come here and this. Okay. They said find y in terms of x. So you're done. You've already found it. So this is your square root. This is your final solution. 9 over the square root of x + one. Then you get your marks.

[00:14:08]So easy cuz they only wanted that. Now we come to here. Y is inversely proport So now they're giving you as a statement. Now they're giving you as a statement. Careful there you write it. Y is proportional. They say it inversely proportional. So it's proportional to 1 / whatever they now say. They say x<unk>x + 2. So roo<unk> x + 2. If it's inverse, we will say one over. We will if they don't say inverse, we just put the stuff. But it's inverse. So we say 1 / the square root of x + 2. Don't make a mistake here. It's illegal.

[00:14:40]Next step, remove this fish. Put an equal sign. So you put an equal sign.

[00:14:44]Then you put K. So it'll be K over the square roo<unk> of X + 2. Then now what do we do? We have been given the X.

[00:14:51]We've been given the Y. Put them remove K. We don't want K. He is an enemy.

[00:14:59]Enemy number one. So you're going to say let X be equal to 2 and Y be= 3. So now you're going to say where there is y we are putting three is equal to k over the square root of where there is x you are putting two. So 2 + 2. You now say 3 is equal to k over the square<unk> of 4. 3 will be equal to k over roo<unk> of 4 is 2. You take two to the other side. You are going to have 3x 2 is equal to k which is 6 is equal to k. So 6 will be equal to k.

[00:15:33]Now are you done? Yes, surely you are not going to end here. When you find K, come and remove it from the equation here. Now, so you now say Y is equal to instead of K, you now say 6 over the roo<unk> of X + 2. I'll say what a smart person. Well done. So you now put here 6 over the<unk> of X + 2.

[00:15:55]Are we together students?

[00:15:58]Are you seeing this?

[00:16:01]Students, are you seeing this?

[00:16:06]Okay, well done. Now you come to here.

[00:16:09]Why is directly don't let no words cost you. You are you know what to do. You know the steps. Read the thing from the first line and convert it to a relationship. Y is directly proportional. So you don't put any one over. So you put Y. Then you put your fish is directly proportional to what?

[00:16:27]Square root. Don't ignore the square root. Don't pretend you didn't see it.

[00:16:31]You saw it. It says square root of that.

[00:16:34]So put the square root square root of x + one. There we go. Now they're directly proportional. Now there's no one over anything here. We didn't put one over anything cuz there's no word inverse here. Got to get rid of the K. Now we hate him. We don't hate him, but we don't want him there. He is a massive disturbance that guy. So get him off there. How do you get him off? You now need to remove by putting these. You know your 10.5, you know your eight. So you say let Y be equal to Yes, you can ask the question. Somebody wants to ask a question.

[00:17:12]No question. All right. So Y will be 10.5 and X will be 8. Yes, you can ask the question.

[00:17:33]Well done. Well done.

[00:17:35]Let's go. Now we say y is 10.5, x is 8.

[00:17:39]So now remove where there is y. Please put 10. Don't mix it up. Don't you make such small mistakes. You are too old for that. Where there is y, put the y. Y is 10.5. So don't mix it. Don't take eight and put on ah you. No, you can't do that. So y is 10.5. So put 10.5 there.

[00:17:56]So you say 10.5. Be careful.

[00:17:58]is equal to k then the square root of where there is x you actually put the x which is 8 so it will be 8 + 1 be careful you now say 10.5 is equal to k * roo<unk> of 9 pardon pardon you now say 10 where are we getting the k we are getting the k at this step when you remove a and you put an equal sign, you have to put K or else you are wrong. You have to put K on the right hand side when you put an equal sign. Okay?

[00:18:42]Yes, you can ask the question.

[00:18:55]No, we ain't going to do that. That's a different one. This last sentence, we are only coming to it if we have removed K.

[00:19:05]So, we are not even looking at this one right now. This one is we are not even looking at it. We are not going to put X equal to 8 there. That's a different one. This statement of X= to 1.56, we are not working with it right now. Right now, we want to get rid of K. Root of 9 is three. So, K by three. Did you hear me? Tell your mind this tell that mind of yours to say when you remove a fishaba I'm talking to your mind now not to haba not to the eyes direct to the mind listen tell your mind when you remove the fish and put the equal sign you are forced by maths which you can't break unless you want to fail you are forced by maths it's a rule that when you remove the fish and put an equal sign You have to put K or else you are completely wrong and we don't know what you are writing. We are not going to look at your work. So when you remove the fish, tell the mind it's hard. It's hard. So I'm I have to do it like this.

[00:20:05]Tell your mind everybody right now when you remove this fish and put an equal sign. If you don't put a K, then I don't know what math you are doing. The math you are doing, I don't identify with it.

[00:20:17]If you put an equal sign, I want to see a K. And you now have to find that k by now saying y is 10.5. So you say let y be 10.5 then x is 8. Then you say x equal to on the next step.

[00:20:32]So now you remove the y you put 10.5 where there was y where there was x you put eight. Then you solve solved until you find k. Then when you find K, you rewrite this equation that had K, but now you'll be removing it and putting its actual value. Come on guys. So now you have three. You take three to the other side. 10.5 / 3 is equal to K. What is 10.5 / 3? Tell me what is 10.5id 3?

[00:21:05]3.5. So 3.5 is your K. Well done. Now remove it here. You're done. Good job.

[00:21:12]So y is = 3.5 multiplying uh the square root of x + 1. Then now you can come here. Now once you have this which has no k the only way of get getting rid of k is by knowing its value then removing it. That's the only way. Now when you have it like this you are a boss. You are an amazing person. You are ready to solve any question. Here they are saying find what what they're saying find y when x is this. So they're telling us the value of x. We come we put here on x then we see what answer for y we will get. So we will now come here and we say let x be equal to 1.56.

[00:21:53]We will now say y is = 3.5<unk> of 1.56 + 1. Don't make any mistake anywhere. Remember to rewrite this. But remember to remove k and put what k actually is. Then now you can answer this one. So you will now put let x be then you now say y will be equal to this. Don't change my steps. Come on students don't change them. So what is this now? Y will be equal to can somebody punch this exactly as it is 3.5.

[00:22:24]Then you can open your bracket. You say the square root of you say 1.56 + 1 that's 2.56. Can you do that? Tell me what you get. What is y going to be?

[00:22:34]What will be your answer here?

[00:22:44]Okay, you got 7.8 as your y. Let me see if that's the answer. This is number what?

[00:22:52]Uh y is proportional to the square root of x.

[00:22:58]What's the answer?

[00:23:14]Let me punch it.

[00:23:17]So, let me punch it. 3.5 roo<unk> 2.56.

[00:23:22]It's 5.12. Didn't Didn't anyone get 5.12? No. Oh, sorry. I made a mistake.

[00:23:27]3.5 open bracket root of 2.56 close is equal to 5.6. I got 5.6. Did anyone get 5.6?

[00:23:40]5.6. Great. Great. Great. Great. So this is the correct answer. Okay. Any solutions and whatever? Yes.

[00:23:49]Should we continue now?

[00:23:56]Should we continue now everybody?

[00:24:03]This is called variation. This topic is called variation.

[00:24:09]Yes, it's called variation which talks about proportional or variation stuff like that. Let's see here. M is inversely proportional to the square root of t + 2. So m is proportional to one over. Before you read this last part, when they say inversely proportional, you say m is proportional to one over. You say 1 over. You put your fish then you say one over. Now you say what? Square root of t + 2. So roo<unk> t + 2. Are we together students?

[00:24:44]Then now you what do you do as your next step after putting this? You put an equal sign. When you put an equal sign, what's the root? Bring in K. So you put K at the top. If it's a fraction like this, K goes on top. Root of T + 2.

[00:24:59]Okay, it's just multiplying. So it's the same as that other part. So nothing changes. K multiplies the right hand side. Now what do I do here? I've got K.

[00:25:09]I now come to read this thing which they tell me. I'll now say let M be equal to 0.5 and T be= to 23. So where there is m I put 0.5. Don't mix it up. Is equal to k over square root of where there is t they say put 23. So you say 23 + 2. So you now get 0.5 is equal to k over 23 + 2 is 25. So roo<unk> 25. You get 0.5 is equal to k over 5 because root of 25 is 5. You take 0.5 * 5 is equal to k because 5 goes to the other side. It will now multiply to get K. You get 2.5 = to K. So my K is 2.5. Well done. You now come and replace in this equation.

[00:25:58]So you now write M is equal to instead of K you put 2.5 / the square root of T + 2. Are we together?

[00:26:16]Hello everybody.

[00:26:23]Okay, well done. Now what do we do here?

[00:26:27]Now what do we do? We can now answer any question because we no longer have K. We have an equation. Everything is good.

[00:26:38]Now you can come to this one now which said find M when T is whatever. So you just go be right. You say let t be equal to 98. Then m will find itself. m will be equal to 2.5 over the square<unk> of 98 + 2. So m is equal to 2.5 over the square<unk> of 100 which is going to be m. What is your m now? Is going to be 2.5 over 10. Your m will be 0.25.

[00:27:08]There we go. 0.25.

[00:27:12]We are going to get the best results in the whole world. Let's keep going.

[00:27:17]What are we going to do here? Just follow the steps. If you follow the steps, you're a powerful person.

[00:27:23]Because you're going to get a different question in your exam. It's going to be yours. It's going to be your question.

[00:27:30]So, respect the steps.

[00:27:33]If you want marks, respect the steps, students.

[00:27:37]Here we've already been given the relationship. You should be able to clearly explain to me what you are doing cuz you're following steps. You tell me, "Sir, I already have the fish here. I already have the relationship. The only thing I have to do is remove that fish of theirs. Put an equal sign." And then I will put a k when I'm putting an equal sign. But when I I first rewrite what they gave me, y is the is proportional to 1 / rootx. I say true. You say I'm going to remove this and put an equal signal sign. I say yes. Then you say when I remove an equals I put K on top of root X like this. I'll say true.

[00:28:12]Then now you have it. What do you do when you have K? You come to this relationship they've given you. You say let X be = 9, Y be= to two. So now where there is X we are putting 9. Where there is Y, we're putting two. Where is Y?

[00:28:27]It's here. We put a two is equal to K over the square root of where there is X we are putting 9. So rootx. So 2 is going to be equal to k over<unk> 9 is 3.

[00:28:37]We take three to the other side. 2x 3 is equal to k. Now 2x 3 is 6. 6 is equal to k. There we go. We now have k. So now we're going to write y is equal to instead of k we put a six. So it will be 6 over roo<unk> of x. There we go.

[00:28:56]6 over roo<unk> of x. Now they said find the value of y when x is 36. You now write here today. Let X be equal to 36.

[00:29:05]Y will be now equal to 6 over the roo<unk> of 36. Y will be now equal to 6 over root of 36 is 6. Y will be now equal to one. So your Y will be one. You get your marks. Come on now. You see you're going to get 100 if you do this for every particular question cuz you're following the steps. So nothing will touch you. You're fine.

[00:29:30]Here they've given you as a statement here. Why is that? Can you write my corrections? If you are in class right now and you didn't write the work, can you just write all my answers, all the corrections, and submit them? You'll get your 60%. It's better than it's better than zero.

[00:29:48]You need it. I told you you need it.

[00:29:51]Y is directly proportional. It's direct.

[00:29:55]So you say y remember direct and inverse it's the same thing you still put a fish but for inverse you would have said one over for direct you don't say one over you just put your fish then you read the second part it's proportional to what x - 1 o so it'll be x - 1 o this first step what a good person steps then now remove that fish of theirs put an equal sign we want an equal sign so you Okay, y is equal to when you put an equal sign the right side now gets a k multiplying x -1 all^2 y will be now equal to uh now that you have your k your k once you have your k you go and read this statement you say now let x be = 4 and y be = 3 so now you're going to say where is y you put three you say 3 is equal to k multiplying where there is x you're putting four 4 - 1 2 3 is going to be equal to k 4 - 1 that's 3^ 2 then 3 is 9 so 3 will be equal to k by 9 you take 9 to the other side 3 over 9 is equal to k 3 into 3 1 into 9 3 is equal to k k is 1/3 so you can now write where there is the equal sign which is on this stage here you remove the k you put 1/3 so you say y is equal to now 1/3 of x -1^ 2 Are you seeing it?

[00:31:36]All right. So now this is going to be it. Now applying 6 squ. Can somebody do that? Multiplying by 1/3 is like dividing by 3 class. So can everybody say 6 squ? Then you say divided by 3.

[00:31:48]What do you get?

[00:31:58]12.

[00:32:00]I got it before you.

[00:32:03]I thought you the ones with the calculator, guys.

[00:32:17]Questions? Anyone?

[00:32:25]All right, how many questions are left?

[00:32:27]Two more. I hope you wrote my corrections. I definitely hope you did.

[00:32:32]Y is inversely proportional, which means why you put your fish then you put one over.

[00:32:39]Inversely proportional to the square.

[00:32:41]Don't come on to the square. They didn't say the root.

[00:32:48]So it is proportional to 1 / then you say x + 3 all^ 2. Are we together? Can you see this square root? If they say the square root, they'll say it. Look at it here.

[00:33:12]To the square root.

[00:33:14]Can you see here? Here they say to the square of x + 3.

[00:33:26]So you do it like this. x + 3 all².

[00:33:28]Which means y is equal to 1 / x + 3 all 2. No k over. Sorry, not 1 /. If you leave the k, you are you're in trouble.

[00:33:41]Now once you have k you say let x be = 5 and y be = 0.375.

[00:33:49]Now you can ducy where there is y you put 0.375 is equal to k over where there is x you put five. So it will be 5 + 3 squared.

[00:34:00]What do you get here?

[00:34:03]0.375 is = k over what is 5 + 3? That's 8 squared. So you can now bring it to the other side.

[00:34:13]0.375 by don't you dare say 8 squ is 16. I'll run away from you. 64 that's 82. It's 64. So it will be k over 64. You can now say 0.375 uh by 64 will be equal to k because 64 will come to the other side to multiply.

[00:34:32]What's 0.375 by 64?

[00:34:43]is 24 is equal to k.

[00:34:48]There we go. Now what are we going to say? y is going to be instead of k we now put 24 over x + 3 2 Last one.

[00:35:10]Y is inverse again. Inverse. So there's one over there. So you say y, you put your fish proportional to one over cuz they said inverse proportional to then they said x squ. So you put your x squ in the bottom. Now what you do? Remove the fish, put an equal sign, but you put the k on the right hand side. It's like this. Now once you have it like this, you use this. You say let x = 3 and y be = 2.

[00:35:38]Now what do we do here?

[00:35:41]Wait, somebody needs to mute the mic.

[00:35:44]I'm not sure where it is. Check everybody.

[00:35:49]I can't see, but somebody has to mute the mic. Check your mics. Check your mics.

[00:35:57]Right? Now we'll be saying um x is 3, y is 2. You now say whether is y you're putting two is equal to k over whether it's x you're putting 3. 3^ 2 is equal to k over 9. You take 9 to the other side. 2 by 9 is equal to k. 2 by 9 is what? 18. 18 is equal to k. So this becomes your k, not the y, your k. So you now rewrite here. Step number two, you rewrite it once you have k. y is now = 18 / x^2.

[00:36:32]Now you can answer any question which is this one. They then ask you find y when x is 2. You just say let x be = 2. y will be now = 18 / 2^ 2. y will be equal to 18 / 4. What is the answer? What is 18 over 4?

[00:36:59]4.5 is it not?

[00:37:03]And you're done. You get all three marks. Well done. You get all three marks and we say to you, well done. That was just so amazing. That's fantastic.

[00:37:14]Are we together students?

[00:37:20]Great. So for this assignment, you've written the corrections. Those who didn't write, have you written the corrections?

[00:37:28]No more hiding. No more hiding. I want my corrections. Let me do one more. The other ones I'll do them tomorrow. I guess I don't want to do mean I want to do similarity.

[00:37:42]Where is the to send? What?

[00:37:55]Yes. You mean Did you write them down? I hope you wrote them down.

[00:38:03]Why? Why didn't you write the other ones? I'm moving too fast.

[00:38:11]Write these ones. Now, write with me on this one. This is the last one, everybody. Then we will do the ones for physics where where you at the lenses.

[00:38:21]So let's do these ones. Are you are you all watching? Let's do these corrections now here for sim for similarity. The past paper questions. Yes. Somebody called my name.

[00:38:40]Oh, okay. I should send what?

[00:38:47]Oh, you want the PDF version of things?

[00:38:52]Okay, still fine. I can send it. I'll send the PDF version. But I Yes, I'll send the PDF version. It's not a problem. Now, write for me this one.

[00:39:01]Assignment assignment two that we are doing today is it's not variation. Now there's a similarity.

[00:39:12]You write and you submit. If you haven't done it, okay, I want to see your submission. It will be now corrections.

[00:39:21]I'll give you a 60%. That's what happens. UN in university there's what we call a sub exam. So sometimes if you don't do well, you get another chance, but you get 60%. You get you get just a pass. For university, it will be 50%.

[00:39:34]Because the C for university is 50, but for IG the C is 60.

[00:39:42]Are you ready to start?

[00:39:48]Hello everybody.

[00:39:53]Right, let's go through it. I want you to look closely so that you see what you should do here. Okay. All right. Good.

[00:40:00]It's a bit of work here. I did this one because it's the harder one. I I want to start with the with the more complicated things. Okay. So, let's go. Let me explain something here. Can you all just write the things that we use? The first thing is that um original length, I'm going to be writing it in in shortcuts.

[00:40:18]You see, times scale factor gives you the new length.

[00:40:24]So sir, what does this mean? Because I can see this sentence of yours that you like to write, but I may never be able to use it because I will not be able to understand. So listen, if you are dealing with I want to be able to say this. If I can make you understand this, my job is going to be done. This is the hard part. Listen closely.

[00:40:43]If you are dealing with lengths in this topic called similarity, they'll tell you that you have similar shapes.

[00:40:50]So, you actually know you are doing the topic of similarity cuz they'll say you have similar shapes. So, once you see the statement you have similar shapes, you are in this topic of similarity.

[00:41:01]So, that's not the problem. The problem is not you knowing you are in the topic.

[00:41:05]The problem is knowing what to do in the topic. The first thing you must know is that when you are dealing with the shapes, you must always find which one you are starting with, which one you are ending with. And I'm going to show you how you know you know which one to use as the original. I'm going to show you just now. Okay. But here's the thing.

[00:41:24]Listen.

[00:41:25]If the thing you are dealing with is length, let's say height or the length of a side, as long as it's length, then the thing that is relating length is called scale factor. So you must write this relationship of scale factor you should say original length with the whatever length that you will decide to be the original. Whatever you decide to be original will always be original. It can't change. Then if it's length then you'll be using scale factor is will be equal to new length. If you're using areas you're going to say whatever you decide to be the original area you multiplied by area factor to get the new area. So if you are dealing with areas surface areas especially surface areas those are the ones you deal with mostly you use area effect. I don't want to see scale factor on areas. That is a severe lack of judgment. You don't do area factor on lengths or scale factor on areas. You are in disaster mode already. Then the last one, original volume times volume factor will give you the new volume. So if you are dealing with volumes or capacities, capacity is volume. By the way, this could be capacity. Capacity means volume. When you see them say the capacity of this container, they are telling you the volume.

[00:42:54]Okay.

[00:42:57]If they say capacity, you are dealing with volume. You have to use volume factor. So say what is hard about this topic from your experience? What do people struggle with? People struggle with this first part of identifying that it's areas you are dealing with and using area factor. People think that it's scale factor for everything which is the biggest lie I've ever seen in the whole world. You can't have a relationship between two areas and you are relating them using scale factor.

[00:43:33]Hey you, what are you doing? Don't you know that's wrong?

[00:43:39]Areas are related by area factor.

[00:43:42]Volumes are related by volume factor.

[00:43:47]Lengths are related by scale factor. So scale factor is strictly for lengths.

[00:43:53]Please you are smart. Stick to this please.

[00:44:00]Now the next thing which you then need to do because the tendency of the mind is your mind doesn't want it to be having different ones. It wants one so that the working is short. But you are wrong. You are not going to create a new version of maths. If you want shortcuts, you are gone sir. Volume has its own, area has its own and length have their own. Period. It will never change.

[00:44:30]So listen now. You have to do this whether you like it or not. Then now when you want to change from one thing you get volumes then they ask you about areas that means you now have to change because for volumes you were having volume factor now you want for areas that means you'll be now using area factor. How do you then change like that? Let's say you had sides now they are asking for areas. You can't use the scale factor for areas. You are in trouble if you do that because scale factor is not for areas. Scale factor is for length.

[00:45:04]So you now have to change again.

[00:45:07]Do I have to change again? Yes, you have to change again. Is there no other thing? Like let's say I don't want to change. You have to change.

[00:45:15]Yes, you have to change. So how do you change? Here is the relationship.

[00:45:19]Watch closely everybody.

[00:45:24]Here is the relationship.

[00:45:28]Give me a second. Something is happening with the network. Here is the relationship for changing. Now you should know that scale factor squared is area factor. You only have to know this. Then you should know that scale factor cubed is equal to volume factor. You should know this one again.

[00:45:49]And you are done. Are we good students?

[00:45:53]Have we agreed guys? Are we agreeing guys and girls?

[00:46:01]Okay. So, this is now how you're going to be moving from one to another. You'll be using these two relationships. So, make sure you write this relationship down and this one. You know them. If you know these, then come on now. You're good. Ma'am, you are good.

[00:46:20]So, you come here. Let's now see the steps because now I've given you the info. Now, we need questions. Questions bring experience. Experience brings perfection. So now let's use a question.

[00:46:34]Sir, how do we do it? Listen to the steps. I always love steps. I love steps. Steps solve things. Listen to this. The easiest question that you can ever get is if you see the word similar, remember we are in the topic of similarity. So I said they are going to say something about similar. So for you to know that this is now a question of similarity. You will see the word similar. So here they have used that word similar. So we know we are in similarity.

[00:47:07]Now listen, if they give you these two shapes like this, this is actually the easiest version because you are only dealing with sides.

[00:47:19]You are only dealing with lengths.

[00:47:22]There's nothing to do with area here.

[00:47:24]There's nothing to do with volume here.

[00:47:26]But other questions can actually bring you a mix. So this is actually the easiest one. You don't fear this one.

[00:47:33]This is the easier one. What you do, listen now. Listen to what you do.

[00:47:40]There's going to be a small side and there's going to be a big side. So here is the rule.

[00:47:48]Listen, we know that we are dealing with sides.

[00:47:53]So we are going to have OG * scale factor is equal to new. Why scale factor sir? Because we are dealing with sides.

[00:48:03]Now who is going to be the OG one in this case? It's going to be the small one. The small one is going to be the original one. Do you know why?

[00:48:14]Because the the one you make new is the one that has something missing.

[00:48:21]You're going to listen to this rule.

[00:48:24]It's going to work for you forever from now until forever. The one which has something that is missing. It be the one which goes this side. It's the missing one. So we are going to use that idea.

[00:48:37]Let's now get to work. So I'm going to come here and I'm going to see ah all right. So this one has this side which is missing. So it's the one that is going to be the new and it's the larger one. So, what I'm going to say, I'm going to say small, I'm going to say the length of the small, okay? Because that's the original one times the scale factor should give me the length of the large.

[00:48:59]You've you're good. Well done for doing that. Now, you're going to pick choose which length of small do you want to start with. You start with this one because you also know the length on the large because you want to find the scale factor. So, what length of small do we have? 10. So you say 10 * scale factor which you don't know is equal to the same length on the large shape the same length which is here 45. So a length on the small one 10 times the scale factor.

[00:49:25]Why scale factor? Because we are dealing with sides lengths is going to be the same length on the large one. Why did you put large on this side? Because it's the one that has a missing side that we will find in step number two. So we started with this 10 because we have him here 45. We can't start with 14 because we don't have him. He's an X. We don't have him. We can't start with him. So now look at it. You're going to say 10 times scale factor. You now say scale factor is equal to 45 over 10. The biggest secret to success is you mustn't panic. And the only way for you not to panic is you follow steps. So you look at your shapes. You see is it the small one? You're going to do this for about 10 questions. We have questions below this. So you're going to get better as I keep doing. So just listen closely. As I keep doing, you are going to get better.

[00:50:15]The secret is the one who has something missing is the one we will put on the other side. Anyway, it could be the small one. It could be the large one. I don't care. You don't care. The one who goes on this side is the one who has something missing. And it could be scale factor. It could be area factor depending on what we are relating. Are we relating areas? Are we relating volumes? Are we relating length here? We were relating length. So we used scale factor. So now you are going to say therefore your scale factor is equal to 45 / 10. That's 4.5. You have your scale factor. Then you rewrite this same statement because you want to use it again. The length of the small one time scale factor is equal to the length of the large. Now what is the length of the small? 14. We now want to find x, right? So we now say 14 time what's the scale factor you just found it 4.5 so now you can continue is equal to what's the length of the large x you know if you get in the exam then you try a shortcut to quickly get x you are in serious trouble so now you're going to now say 14 * 4.5 what are you going to get what's 14 * 4.5 good 63 mm is equal to x. Then you leave.

[00:51:39]You know if you go out of exam of an exam having written things like this, you will be the most confident person I know because you know you followed rules. You know you got it correct.

[00:51:52]So look at this second one. I want to I want to grill there's something I want to grill in you which will help you solve this one because this can be a tricky topic. This can be a tricky topic if you don't follow steps.

[00:52:09]Okay, I've scrolled up. Mhm.

[00:52:37]Have you seen it?

[00:52:47]Great. Now let's go to the next one.

[00:52:50]Question number two.

[00:52:53]The the surface areas of two mathematically similar. Hey, you in an exam, you see the word similar, you say, "Ah, sir told me we are dealing with similarity." Okay, similarity. Sir told me we are dealing with similarity.

[00:53:09]So when you are dealing with similarity, you should know in first step what have you been given for both shapes. Here they've told you the surface areas. So you've been given areas. So you're going to be dealing with area factor. Listen closely here. So you are dealing with areas. Oh, so I've been given two areas.

[00:53:33]One will be small, one will be large.

[00:53:35]Look for it. This one is obviously the smaller one. Then this one is obviously the large one.

[00:53:42]So now you want to know which one is original, which one is new. Come here and look at the question they are asking you. Find capacity. We said capacity is volume. Find volume of larger.

[00:53:54]So who who has something missing? Don't worry about the fact that they want volume. Whatever. We are not yet thinking about volume. We know that they will want volume. But that's not what we are looking at. Listen to what you look at. You look at what in the first step.

[00:54:13]What have you been given for both?

[00:54:17]You've been given areas. You know the area of the small one. You know the area of the large one. But now you want to know am I going to say area of large time area factor is equal to area of small or am I going to say area of small time area factor is equal to area of large. What do I do? You see who has something missing here? The larger container has a missing volume. So he will be the one that goes alone. So you're going to start with the small one because he has everything. So you say area of small times area factor.

[00:54:57]Why am I using area factor? We are dealing with areas. This will give me area of the larger. Sir, why did you put larger one this side? Because we know in step two we will be looking for him. He is the one who has something missing.

[00:55:15]Don't change.

[00:55:17]So now what you're going to say is what is the area of the small one? 124 124 times do I have the area factor? No, I say AF is equal to do I know the area of the larger one is 279.

[00:55:33]Then now I'll say area factor is going to be 279 / 124 and I can get my area factor. What is it going to be?

[00:55:43]What is the area factor going to be?

[00:55:48]What's 279 divided by 124 class?

[00:55:56]255.

[00:55:58]Pardon?

[00:56:01]2.25.

[00:56:04]So now look at what you then do. Look at what you then do.

[00:56:09]You now say next step wants volume. So I need volume factor. The only way to get volume factor you need to change area factor into volume factor. How do you do that?

[00:56:20]You use the two relationships. You first since you have area factor you first say scale factor squared is equal to area factor. Now you want the scale factor.

[00:56:30]You already have the area factor. So you take this squared. You take it to the other side. You now have scale factor being equal to the square root of area factor.

[00:56:42]Which means scale factor is equal to the square root of 2.25. What is the scale factor going to be class?

[00:56:50]What's the square root of 2.25?

[00:56:58]1.5. That's going to be your scale factor. Now you want to change it to volume factor. You now say scale factor cubed is equal to volume factor. So you should know this relationship. Scale factor squared is area factor. And this one scale factor cubed is volume. And you should know how to use them. Here we are using them now to come from area factor to volume factor. You now say scale factor cubed is volume factor. So you now say 1.5 cubed gives you your volume factor. What is 1.5 cubed?

[00:57:26]Somebody.

[00:57:30]It's 3.375.

[00:57:32]Right? This gives you the volume factor.

[00:57:36]So now you have volume factor. What do you do? You are ready. You now say volume of small because you had said area of small. So volume of small times volume factor is equal to volume of large. Don't change the order. If you had is going to be volume of the larger one. So volume of the smaller one. What is the smaller one here? Capacity of the smaller container which is the volume of the smaller container 56 m times the volume factor 3.375.

[00:58:06]This will give us the volume of the larger one. What is it going to be? 56 * 3.375. What do you get?

[00:58:21]What do you get students?

[00:58:26]189 m. This is going to be the volume of the large. So 189 m. Are we together?

[00:58:36]This becomes the volume of the large. Is this hard?

[00:58:41]No, it's not hard. We come here. Two mathematically similar. Ah, we are in similarity.

[00:58:52]Okay.

[00:58:54]Now, what is it that I have for both containers? Solids have volumes this and this. Obviously, this is going to be the larger one. And obviously this is going to be the smaller one because it has the smaller volumes. And what you have is volumes. So you have volumes of both.

[00:59:12]But so now obviously since you have volumes of both your first sentence is going to be on volumes. It's going to be something times volume factor gives you something. But then you need to see in step number two what you will be looking for. You'll be looking for height of the larger. So since you're looking for the larger one again in this question larger will be alone. So you're going to say since you have volumes you start with the volumes. Volume of smaller times the volume factor gives me volume of larger.

[00:59:49]Now what is the volume of the smaller?

[00:59:51]4.8 times what's the volume factor? We don't know. Gives me volume of No, sorry it's not 4.8. Volume of smaller is 24 here. 24 cubic centimeters. Okay, if you want to put the units times volume factor gives me volume of larger 81 cm.

[01:00:09]Now how do I get volume factor? I take 24 to the other side. I have volume factor is equal to 81 cm divided by 24 cm. What do you get here as your volume factor?

[01:00:22]Very very strong students. What are you going to get here?

[01:00:28]Okay, wait. YouTube quantum pulse. You said you have a doubt. Explain the question. It's what? What do you get as your volume?

[01:00:42]3.375.

[01:00:47]You can even leave it as a fraction if you want, but 3.375 is not a bad one.

[01:00:51]So, you can leave it as that. Normally, I would have left it as a fraction, but you can leave it as 3.375. It's still fine. So now what you're going to now do is you say the uh what is 3? What is if I reduce to lowest terms? What is 81 over 24 when you reduce to lowest terms?

[01:01:07]Somebody put in your calculator and tell me what you get.

[01:01:23]Am I still in the lesson?

[01:01:33]Can you all hear me?

[01:01:41]Okay.

[01:01:44]It's 3 over 8. Good.

[01:01:47]It's 3 over 8 or 8 over 3. What is it?

[01:01:55]3 over 8. No, you mixed it up. 81 over 24 or three and 3 over 8. Press second function then say a b over c. I want it as an improper function.

[01:02:20]Okay, let's just keep it as three. Okay, wait. It's dangerous. It's dangerous.

[01:02:25]Let's keep it as 3.375. I don't want any mistake here. So now, okay, that's good.

[01:02:29]We have volume factor now. But we see on step number two, we are going to be looking for the height of the larger solid, the height. So that's a length.

[01:02:38]So we're going to need scale factor. So we need to change from volume factor.

[01:02:41]Anyway, we only have that one method. We know scale factor cubed is equal to volume factor. This is the relationship between scale factor and volume factor.

[01:02:49]So you now take cubed to the other side.

[01:02:52]Scale factor will be the cube root of volume factor which is going to be the cube root of 3.375.

[01:03:01]Somebody can you tell me what you get as the scale factor? Scale factor is equal to what?

[01:03:07]Say second function then put then press this x cubed. It becomes cube root. Then say 3.375 what you get?

[01:03:23]Oh, Simon, I'll help you. I'll help you.

[01:03:25]I'll help you, Simon. What do you get?

[01:03:30]1.5.

[01:03:33]So, this is 1.5. So, now we can write the last one. We can say height of small times scale factor because we are now dealing with lengths.

[01:03:53]Are we together?

[01:04:00]Okay, give me a second. Seems like one of my lives has been disconnected.

[01:04:57]right? Let's finish it. If you can stick to these tips, then I know you're going to be safe. Okay. Should we finish? Can we go on?

[01:05:08]Can you all hear me, guys?

[01:05:18]Okay, my network is not the strongest.

[01:05:20]My the my the place where I put my styling has a bit of obstructions because I changed locations.

[01:05:27]So, you forgive me. But anyway, it will be better. It will be better. Let's let's continue now. What are we saying this? You now say what is 4.8 * 1.5?

[01:05:36]What do you get?

[01:05:39]You'll be now done. What is 4.8 and a * 1.5 7.2 and this is cm is equal to the height of the larger. So can you see that the steps are actually not a lot.

[01:05:54]Just look at how many things we wrote. H it's just a few sentences just these ones and these ones. The hardest thing is to tell your mind the steps to do because it has its own. You have to fight it. Trust me. Once I got that message, there's a part where I learned that my problem is my mind. I have to tell it to stick to these laws. Once I got there, I could always get answers.

[01:06:20]Tell your mind that the only way to come from volume factor to scale factor is this one.

[01:06:28]If you leave it alone, your mind will tell you there's another way and it will lead you to being stuck because it will tell you there's another way. And then when you ask it what other way, it doesn't have. So tell it, hey man, the only way I'm going to change from volume factor to something else is to remember the relationships. So you have to remember these relationships, man. Scale factor cubed is volume factor and scale factor squared is area factor.

[01:06:56]I should just have them in case I need them.

[01:07:00]Make your mind have them. They're the powerful things.

[01:07:08]Antony, shall we together?

[01:07:15]Good.

[01:07:17]Here's another one.

[01:07:19]Slow down. Look at this shape. What did I tell you? I told you that this part A is the easiest where they give you some side and they ask for another because you are just going to be using relationship between one side to get relationship between another side. You don't have to change from volume factor to area. There's no changing here. We are only going to use scale factor cuz the only thing we have is sides for these two things. So this is the easiest one. Now, what we just have to find out is which of these shapes, the bigger one or the smaller one, which one has something missing? Which one has this PR that they're looking for? Is it the bigger one or the smaller one? Tell me, where is P R students? Is it on the bigger shape or on the smaller one?

[01:08:08]On the on the smaller one. So, the smaller one is the one going to its own side. Don't change it. So you and since we are dealing with lengths, we are working with scale factor. So you're going to say length of larger time scale factor is equal to length of smaller. Please I hope you are obedient people who will follow the steps.

[01:08:35]Now let's start with a length that we know on both sides. Which one do we know? We know this one where it's nine and here where it's six. So we can say length AB it's the it's a length on the larger one times the scale factor should give us the same length on the smaller one which is length PQ on the smaller one it's called PQ. So what is that length AB? It's 9 time scale factor gives us the length on PQ. What is it?

[01:09:02]It's six. So now we will say scale factor is going to be 6 over 9. And your scale factor will be equal to 2. 3 into 6 that's two. 3 into 9 that's three. So it's 2 over 3. This becomes your scale factor.

[01:09:19]Then you do the same relationship here.

[01:09:22]Length of larger time scale factor gives me a length of smaller.

[01:09:27]Stick to the plan. Length of larger. Now that you know scale factor, you are very powerful. Is equal to the length of smaller.

[01:09:37]What is the length of the larger one?

[01:09:40]Which is the same as P R. P R is this one. So on here it will be 12. So you say length AC * scale factor gives me length P R. What's length AC? 12 times what's the scale factor? 2 over 3 should give me length of P R. Tell me what is 12 * 2 over 3? You say 12 * 2 then divided by 3. What do you get? You get 8. 8 cm is equal to length P R. So you just come and you say here 8 cm and you get your two marks. Do you see?

[01:10:14]We are strategic. We follow steps.

[01:10:17]That's why we know we will get all answers because we are people of steps.

[01:10:23]I'm teaching students of steps.

[01:10:26]Let's come to this one.

[01:10:30]Triangle ABC and triangle PQR. So it's the very same triangles.

[01:10:37]Now they are saying here they are mathematically similar. Yes.

[01:10:42]the volume and they want volume of the larger one. Now, so look at what we do here. Be careful, right? Since on here the scale factor that you found this 2 over 3, you found it by saying length of larger. So you're not going to change first of all change it to volume. You say scale factor is equal to 2 over 3. scale factor cubed will give me volume factor.

[01:11:15]So 2 over 3 cubed will give me volume factor. 2 cubed 8 3 cubed 27. This gives you volume factor. Volume factor is 8 over 27. Now since you said length larger time scale factor, you'll be now saying volume of larger times volume factor gives volume of smaller because you started with larger on scale factor. So you must start with larger on volume factor or else you are lying. So now what is the volume of the larger one? We don't know. We don't know it. Volume of the larger we don't know it. Times what's the volume factor? 8 over 27. This gives me the volume of the smaller. They told you the volume of the smaller it's 1120.

[01:11:59]Now you take 8 over 27 to the other side you have volume of larger. When you take a fraction to the other side it will be 1120 times the fraction will flip 27 over 8. Then you'll get the volume of the larger. Can somebody tell me how you get volume of the larger? Say 1120 * 27 then you say divided by 8. What do you get?

[01:12:23]Say it. 1120 * 27 then divided by 8.

[01:12:27]Tell me what you get.

[01:12:35]3,780 cm. 3,780 cm.

[01:12:43]Are we together everybody?

[01:12:51]Okay.

[01:12:54]I want all my corrections.

[01:12:59]All my corrections.

[01:13:01]One, two, three, four, five questions left. Let's do this one.

[01:13:09]Let's do this one. We'll be done in 10 minutes, I guess.

[01:13:15]Right. What I want is steps because you're going to be stuck again. This is the beginning. The beginning of every question is tricky.

[01:13:24]Laura leak.

[01:13:28]The beginning of every question is tricky. I know that.

[01:13:32]So that is why I'm grilling into you how to start. Don't run away.

[01:13:40]Fight until you are confident of how you begin.

[01:13:44]I look at these two shapes. Listen, what I'm looking for is what have I been given for both shapes because they are going to change the structure of the question and everything cuz I'm going to see the word similar and I'm going to know similarity.

[01:14:03]My first thing is what have I been given for both shapes?

[01:14:09]Surface area se surface area of B. So I've been given areas.

[01:14:17]This is the smaller one.

[01:14:20]Here they are calling it A and B. Yeah, smaller. This is larger. We can still call it A and B.

[01:14:28]Okay. So we have areas. So we are going to deal with the area factor and areas in the very first sentence. But now we want to know which one has something missing. It's B. B has something missing. So we are going to say area of A times area factor is equal to area of B. Why are we putting area of B on this side? Because he is the one that has something missing on step number two.

[01:15:00]Oh, so because he is the one who has something missing. He's the one who goes alone. Yes, he's the one who goes alone.

[01:15:07]Okay, sir. That's fine. But why did you do areas? because those are the ones we are given for both shapes. Step number one, you don't start with what they are looking for. You will never find it. You start with what you are given for both shapes. You've been given areas. So we are doing areas. And who do we put on his own side? The one who you are going to need in step step two. So now what is the area of A? Huh? A is the smaller one here. The area of A. This is the area of B. Area of a is 60 times area factor we don't know it yet is equal to area of b which is 540 area factor so this if you want you can say 60 cm squared will give 540 cm squared area factor will be 540 cm squar divided by 60 cm squared what do you get area factor will be the zeros cancel 6 into 61 into 54 is that 9 area factor is nine with no units. Area factors, these scale factors, area factors don't have units. Now, since you want scale factor, you take this square to the other side. Scale factor is the square root of area factor, which means scale factor is equal to the square root of 9, which means that the scale factor is equal to three.

[01:16:25]Now you can go for it. You now say height since you had said area of a, you now say height of a time scale factor.

[01:16:32]Now, because you're dealing with lengths, will give you height of b. What is the height of A? Do you have it? Yes.

[01:16:38]Seven. So seven * What's the scale factor? Do you have it? Yes. Three. And it's 7 cm by the way. Is it going to height of B? What is 7 * 3? 21 of what?

[01:16:48]Cm is equal to the height of B. So this is 21 cm. Thank you for your attention to this matter. Are you seeing this?

[01:17:04]Okay.

[01:17:09]Look at this one. Can somebody tell me what is the first step? What do you look for in step number one? The information that you have been given for both shapes. Right? Is it volume? Is it area?

[01:17:22]Is it length? Surface area. I'm not even the moment I read the word similar.

[01:17:26]Look, you don't get marks because you are reading this way. The diagram shows two mathematically similar solids. The surface this is the way you guys have been reading since standard one and I don't want to see it.

[01:17:45]I I'm not into I'm into results, guys.

[01:17:51]Anything that has a chance of lowering your results, I don't want it.

[01:17:56]You reading this the way you were reading in primary and lower secondary and all this time is deadly because you are filling your mind with details that don't that are not important.

[01:18:11]What is important is for you to see the word similar.

[01:18:17]You skim in questions. You look for what topic it is. So you see the word similar. You know you are in similarity.

[01:18:27]Now if I am in similarity I have to find what has been given for both shapes.

[01:18:37]Surface area of the larger and surface area of the smaller. Oh, so I'm going to be relating with area factor here.

[01:18:45]Surface the area of of the larger by area factor giving area of small whatever. Now you see which one has a missing thing. You know you're going to be relating using area factor. Fine.

[01:18:58]Which one is a missing thing? It's the smaller one because it will have a missing volume. So that means he is going to be alone. So you are going to say area of larger time area factor gives you area of smaller.

[01:19:20]Are we together? Why did you use areas and why didn't you use volumes? Because volumes are for step two. Areas are for step one because that's the one we've been given for both. So now what is the area of the larger? You look there's 200 and there's 98. Obviously the other one is 200. So 200 cm squared times area factor gives you the area of the smaller one. 98 cm squared.

[01:19:46]How's that?

[01:19:48]Now what do you do to get area?

[01:19:58]What do you get now? You say area factor is equal to 98. This is cm squ divided by 200 cm squ which is going to be what is 98 divided by 200.49 is it exactly 0.49 49. If something which is not exact, what is the square root of 0.49, guys?

[01:20:39]0.7.

[01:20:43]You said 0.7. Okay. Thank you.

[01:20:54]So now let's go for it. We will now say we don't want we want volumes. So we now want volume factor. So scale factor cubed will give you volume factor. What is the scale factor cubed? 0.7 cubed should give us volume factor. What is 0.7 cubed? What is it?

[01:21:15]Can you now do it? Because we now want volume factor.

[01:21:20]3 point 3.43 is the volume factor oh 3.343 is the volume factor. Now you're going to just say since you had said area of larger you say volume of larger times it's what 0 point oh 0.343. Now since you had said area of larger you say volume of larger again but now it times volume factor gives you volume of smaller.

[01:22:02]So what's the volume of larger? You go and you check here the volume of the larger solid is this. So you now say 450 * what's the volume factor? 0.343.

[01:22:14]This gives you volume of the smaller one. Volume of smaller.

[01:22:19]What is it? 450 * 0.343. What do you get?

[01:22:30]It's what?

[01:22:35]What will be the answer? Say it.

[01:22:43]Yes. Tell me what's the answer, guys.

[01:22:50]154.35 volume of smaller.

[01:23:01]Any question?

[01:23:10]Thank you.

[01:23:16]Well done.

[01:23:20]Okay, these last two I'll give you to try. I need to give you to try. So for Mets, we end here, right?

[01:23:28]Yes.

[01:23:29]for Mats. I think I'm proud. I'm happy with where you are. You try these last the last two which is this one. The last three rather and this one and this one.

[01:23:43]You try submit as my corrections. If you have forgotten the steps, come back and watch the video and until you remember the steps. Are we together?

[01:23:56]Yes, Blinky. I see you. Blinky, you've got a question.

[01:24:00]No, no, Blinkcky. It's not pre-recorded.

[01:24:04]Um, no, it's not pre-recorded. It's not pre-recorded, Blinky. I'm I'm in a lesson with my class and I'm streaming on YouTube.

[01:24:14]So, I'm actually in a lesson with people. Okay, Blinky.

[01:24:25]All right, so this is it.

[01:24:27]I I I let me stop the streaming here.

[01:24:30]This is the last question I'll do for this. Um and then you can go back and check all the ones I did below. Class, please do the uh the last three. Those who are in my class, please do these last three and if you haven't done them and fix Okay, Blinky, I'm about to stop the live video. I want you to go behind and rewatch what you missed and then you'll be fine. Okay, you just go to my channel, then go to live videos, you see it.

[01:25:01]All right, everybody. That's it, right guys?

[01:25:06]Antonia for Mats. I'm ending here. I'm going live to do the bio solutions now.

[01:25:18]Let me check the register first. Mark the attendance.

[01:25:29]Hi, Hassan.