The Ultimate Year 8 Final Term Revision

Added: 2026-05-14

[00:00:00]Hello, your final exam is up and you have to revise for your exam. So I have arrived this video and this is your ultimate video for revision if you are studying in year 8. Let's start.

[00:00:16]So we have the first thing here uh being included in your exam which is how we convert between fractions into a a a how convert fractions into percentages.

[00:00:29]decimals and mixed numbers if needed and this will drive us to what is a number. So a number has a lot of a lot of a lot of uh uh a lot of let's say uh categories that we can follow. In this case we have the first thing which is being as a fraction. Let's forget not not forget about being an integer or let's say a whole number or also it can be a decimal. Decimal also case here.

[00:01:01]Okay. So number also can be presented as a percentage. uh when we have the percent sign of course also can be presented as a percentage uh this being taken in consideration. Uh but here we have a fraction and we need to change it into these you know as you know the fraction can be classified into three things. It can be a proper fraction, it can be improper fraction and it can be a mixed number. Okay. So it can be also a mixed number there. All right. Uh the proper fraction is the fraction that you cannot change into a mixed number. This cannot be happening.

[00:01:40]The improper fraction is the fraction that you actually can change into a mixed number. Um the improper fraction basically when you have a numerator bigger than denominator. The proper is actually the qu opposite which when you have a numerator smaller than the denominator as you can see. So we have here three types here. I just showed you the classification. Now we're going to do what actually you're going to have to understand. So this this here it's a fraction. It is 5 /2. Well I understand that this kind of fraction is improper because the numerator is bigger than the denominator. So this actually can be changed into mixed number because the question asked me changed into mixed number if needed and actually here it is needed and also I'm going to change it into a percentage uh and a decimal number. The first thing I'm going to be showing this fraction is as a mixed number because it's the best thing to do here as a beginning. um 5 over two. You can you can do the first method which is basically 5 over two is the same as having what? It's the same as having 4 over two and 1 / two which is basically two and a half, isn't it? Because 4 / two 4id by two is going to be two and we have the half. But also there's another method to to to change this into a mixed number by using the long division. 5 over two means what? It means 5 / two.

[00:03:18]So you're using the long division. This part here guys after the division sign we call it the divisor. This part here is called a dividend end because it becomes it comes at the beginning. And this one here calls it the divisor.

[00:03:31]Okay? So basically whatever you have here just put it there. in this here and whatever you have here on the left we put it inside as you can see. So what is the number you multiply two gives you five. There isn't. But there's a new number though which is four. 2 * 2 is four. You subtract. Here you go. You have one. So my whole number is two. So I'm going to write it down. My remainder which is very important to you to know that the remainder here is going to be one. So it's my numerator. So this one is my numerator. Why? Because it's the remainder. It starts with r and we have an r in numerator too. So remember that and my divisor is two. Therefore my denominator is also two. D to d divisor denominator. So here you go. I've changed it into a mixed number. Make sure to write this these notes.

[00:04:32]You can pause the video and write them down and try them yourself. Let's go.

[00:04:42]So the first thing has been done which is changing this into mixed number.

[00:04:47]After we did our method, it been showing that it's two and a half. Now let's take this fraction and show it as a decimal number. So how can we do that guys? How can we show this as a decimal number having a point in it? The same thing by using long division. 5 over two is the same as 5 / 2. So when I do the long division, 2 and 5 is going to be here, which is one going to be here. 2 * 2 is going to be four. You subtract, it's going to be one. I don't have a number uh which is one as a multiple in times table of two. So therefore, I'm going to be uh having to add zero here and point up there. What's the number multiply to gives me 10? Actually, it's five. 5 * 2 is 10. Subtract 0. Here you go. My final answer is 2 and 1/2. So this is basically 2 and 1/2. So my decimal number is 2 and 1/2. Make sure to pause the video and write down yourself and check it out. All right. So decimal number here would be 2 and 1/2 2.5. And the last thing here we're going to show it as a percentage.

[00:06:00]When you show this as a percentage, you have two maneuvers. either taking the fraction multiply by 100 or just simply take the decimal which is be would be way better when you take the decimal here in this case 2.5 and whenever you want to change into a percentage to give it the percent sign you have to multiply by 100 so you multiply by 100 so whenever I want to change into a percentage I multiply by 100 yes repeat the video if you don't understand whenever I want to change the decimal into a percentage I multiply by 100 even if I want to change the fraction into a percentage I also multiply by 100.

[00:06:33]Anytime I want to change it to percentage, I multiply by 100. And after when you do this, we multiply by 100.

[00:06:39]The multiplication sign means going to the right. So I start from a decimal point here. The multiplication sign means going to the right. How many jumps though? Since I have two zeros here, I'm going to have to jump two jumps. So let's go, guys. One to cancel the point and another one to add zero. So here you go. It's 250%.

[00:06:59]So one to cancel the point and another one to add zero. So my answer would be 250%.

[00:07:05]That that's that guys called a a a a percentage.

[00:07:12]So this one here uh the second one is also is also a mixed number. Okay. Uh sorry is also improper fraction. So it can be changed into a mixed number. And after you do the long division and everything by yourself, you're going to check it out yourself. You're going to know for a fact it's actually 1 over 30, isn't it?

[00:07:37]It's actually what, guys?

[00:07:40]When you take it, take 31 over 30. Okay, you think of two things. Very good. 30 over 30 and leaving 1 over 30, isn't it?

[00:07:50]So, this will become one. So my final answer would be 1 and 1 over 30. But if you want to do the long division method, that's all right. It's fine by me. 30 here, 30 one here. The nearest is 1. 1 * 30 is 30. Subtract is going to be one.

[00:08:03]My whole number is one. My remainder is one. And my uh um denomin divisor which denominator is 30. So the answer has a mixed number here 1 and 1 over 30.

[00:08:17]If you want to show it as a decimal, you're going to you have to use long division. So it's going to be 31 / 30.

[00:08:27]So it's the same as having 30 here and 31 there. And when you multiply by one, it gets you 30. When you subtract, it gets you one. It cannot be happening there. So what we going to do in this case? How can we find the decimal part of this? So the first thing is to think of that I don't have a number to multiply to 30 gives me to one. So I'm going to add point up there and zero down. And the same thing here I don't have a number that multiply to 30 that gives me uh 10. So I'm going to have nothing. So I'm going to write zero. And when I when I when I do this I'm going to write another zero here. And the nearest thing that would get me to 100 here, this guys, it's going to be three.

[00:09:14]And 3 * 30 is going to be 90. When you subtract, it's going to be what guys?

[00:09:20]It's going to be 10. And you're going to add zero. And it's going to repeat itself. Three, three, three, and so on.

[00:09:29]Notice something, guys. You are not allowed to use the calculator. This is a very important matter for this question.

[00:09:37]You are allowed though to use calculator in different questions like graphs or something. But I need to see you working out. So that's really important to show me what I did right now. If you didn't understand what I did right now, just all you got to do pause the video and go back and do it yourself. All right, let's go. So my the decimal here is going to be recurring decimal irrational number. So it's going to be 1.033 something. we have three three and actually can be confirmed by using the calculator. So I'm just going to do this. All right. All right. So if I wanted to do this as a percentage, it's really important guys. If you want to do it as a percentage, it's really easy.

[00:10:16]All you got to do is take this and multiply by 100. 1.03 multiply by 100. Uh by the way, we have a lot of threes there. Remember that. So when you multiply by 100 there, it is going to be what? uh going to jump from the decimal point to the right because multiplication two times 1 and two and actually it's going to be 103.33%.

[00:10:42]So that's actually very important. You can confirm this by the way using a calculator on your exam. It's totally fine to confirm and check your answers.

[00:10:50]But remember something guys, remember that you would need to write the the steps for me how you worked it out. It's really important for me to give you the format guys.

[00:11:01]And the quote is very easy. Since this is a actually proper normal fraction cannot be changed into mixed number.

[00:11:08]Therefore, I'm not going to change it.

[00:11:09]It's actually very obvious because it's a proper cannot be changed to mixed number. It's really obvious guys and you have to remember this. So, I'm not going to write anything in this section. As a decimal, actually a quarter is well known as 0.25. But you need to show show me how by doing the long division thingy. Here we have nothing. I add zero add point there. 2 * 4 is eight.

[00:11:33]Subtract going to be two. I'm gonna add zero which gonna be five. And this is how you got to do it guys. Subtraction all all the way. So my answer is 0.25.

[00:11:44]So it's very easy guys. We've taken this like forever. So it's going to be very easy for you to work out. As a percentage, all you got to do take the decimal and multiply by 100. Always when you want to change a decimal into a percentage, all you got to do is take the decimal and you multiply by 100.

[00:12:01]When you do that, you're going to jump one, two, two times. It's going to be 25%. Here you go. You got it. 25%.

[00:12:09]So, we jump two jumps because of two zeros. And to the right because of multiplication and we start from a decimal point if we have it there in our fraction.

[00:12:20]This obviously a a improper fraction, an improper fraction. So you do it yourself and check it out. All right.

[00:12:28]So it's really important uh to understand how you convert the fractions in in the best way possible.

[00:12:37]All right. So now we go through uh we go through angles and parallel lines and we have a lot of types of angles. We have this kind of angle which is called corresponding angle angle. Okay. Or corresponding angles. Okay. acres angles showing the letter F as you can see here guys and we have the showing letter Z which is called alternate angle alternate angle or angles because there are two which are actually the same or equal values equal values even this one here vertical or vertically opposite angles vertically opposite angles and they are actually equal.

[00:13:28]So vertical opposite angles and the last one is the co-interior angles. Co- interior angles guys actually they add up to 180.

[00:13:46]So they add up to 180° meaning if I have one of them I would have to subtract 280.

[00:13:51]So I said parallel lines because these actually are parallel lines as you can see. And this one part is equal to that one showing the letter F. We call it corresponding angles. If this was 30, this would be also 30. This is called alternate angle showing the letter Z.

[00:14:08]And if this was 30, this also would be 30 because alternate angles are equal.

[00:14:13]Even if the letter SZ was like this, the angle here would be the same as this angle vertically opposite angle it can be shown in this manner. There are parallel lines obviously this acting in this case. So this this value here would be the same as this value and this value here is going to be the same as this value and they are very important to understand and we have two parallel lines and we have this line here intersecting when you have an angle here and the angle there. They are co inside one shape there guys. So actually between two parallel lines actually we call them co- interior angles and they're not equal actually they add up to 180. So if this was 60 this will be 120 because together they add up to 180.

[00:14:54]It's really important guys. Let's go to some questions about these. The first question says we need to find the value of y. Uh and you show me why you got it like just not just show me the answer like why it's this answer. Obviously it's very pretty simple and straightforward question. The value of y here is going to be 60. Why? Because in the parallel lines rules we have taken off stripes. We have taken the corresponding we've taken the alternate.

[00:15:20]We've taken the vertically opposite. We have taken the co interior angles. Here in this case we have what? Letter zed.

[00:15:25]Sorry it's going to be like something like this. So we have a letter zed here.

[00:15:30]So this value is going to be as this value. When you have a letter z we call alternate angles. Y equals to 60. Why is it equal to 60? because they are alternate angles. You have to write it down and to get the full mark of course. So this one here, this part guys is uh this part we need to find the value of y here also. So if you look at it and you focus this is 160 and if we drew letter f there we can notice that this is 160 also y is 160. So why is 160? Why?

[00:16:07]Because corresponding angle rule corresponding angles let's go we have 70 here in y we need to find the value of y two angles opposing each other in between two parallel lines so co- interior angles they add up to 180 meaning I'm going to take 180 sorry 70 subtract it from 180 as you can see so my answer is 110 guys so y is equal to 110° And here in this case a little bit tricky here guys. I need to find the value of y but I cannot find the value of y without doing some tricky things here. So if you tried doing letter f like you all did now this would be the same as this right.

[00:16:56]So this is what wouldn't work for this one even if you tried as a letter. This has to be equal to that one. Ah mister. So if we did little F, this 85 would be the same as this one, right? Yeah, you're absolutely right. So this is 85 because of corresponding angles because this is corresponding to that. They didn't ask me for this portion, but I did it to find the value of y. This is a straight line, isn't it? So these two add up to 180, right? Because a straight line angle. So uh the value of y equals 180 minus what? minus what? 85 and it's going to be 95 guys degrees. So y is equal to 95°. Why? Because it's straight angles, right? Straight angle. And that's why and we didn't write the reason for the the one before which because it's co- interior angles. Okay guys, you have to write it down. Mr. I'm a little bit confused. Why you did this letter F? What what do you mean by letter F? Okay. Um this is one of the methods you can use but you can also use another one this mister if you think of this mister it's like 180 right so part of it is 85 so if you subtract 180 minus 85 would be 95 so this is actually Mr. 95 you are right mister we need to find this now what do you notice this is the same as this right uh sorry this is opposite this right so they are co-terior angles they add up to 180 you subtract 180 minus 95 this would be 85 and after you do that you do you do like we did now here but mister have another way what what what is it look at this they show letter F No. So actually 95 is why. So you have a lot of a lot of a lot of ways. I'm I prefer this way. I prefer this way guys. I totally prefer this way.

[00:19:04]Okay. I totally prefer this way. This is actually what corresponding to that. So therefore is 85. Subtract 480 you get 95.

[00:19:16]Pause. Go back to the video and choose the method you want. I showed you three or four methods.

[00:19:21]You choose whatever you want. All right, guys. Let's go to this one.

[00:19:26]What's this? It's pretty easy. The value of B. Let's start with the value of U.

[00:19:31]Let's see here. Let's imagine um value of A.

[00:19:36]The value A of A is going to be the same as value of B because they are alternate angles. Let's find the value of B first.

[00:19:41]B is going to be 150. Mr. Y because they are vertically opposite angles. You're going to write it in the exam. Okay? I just don't have time now. A is going to be equal also 150. But but Mr. Y 150 because this here uh is alternate to that one. So it's alternate to B.

[00:19:58]Therefore it's also 150.

[00:20:01]Now let's go to um D. D is going to be equal to 160. Why? Because they are alternate angles. Look. So this is the same as this one. And since this is opposing to C to get the value of C, you would to get something called co interior angle which is add up 280. 180 minus 160 is going to be 20. So C is going to be 20 um 20° guys. Really really really important. Okay.

[00:20:32]Uh frequency table here is very important uh topic. Uh using the frequency table you can find the mode, you can find the range, you can find the mean. Uh the mode is the most repeated uh method and most repeated uh uh uh number. The range is basically the highest minus the lowest and the mean is to total divided by the number of the total. But this works with the usual data. Mr. I don't understand. This is a revision. Go back. You can find one of my videos. It's called averages. Um let me see my channel. What what did I call the video? You can go to my channel on YouTube. Okay. you will find a lesson called averages from tables. It explained the whole this whole thing.

[00:21:13]Okay, but I'm going to do it in very briefly here. So let's find the mode. M mode here when you have tables, you're going to look at the frequency column.

[00:21:21]This is called the frequency column.

[00:21:22]Look at the highest number. The highest number is 10. This is not my answer. So mode isn't 10, but 10 will help me to find the answer. That's 10, right?

[00:21:32]What's next to 10? It's two. Then there you go. The mode is two. So because if the frequency is 10 the more is going to be two as a number of points. So this most repeated point which is two. Uh and you want to find the range guys really important to find the range is basically take the highest data minus the lowest data. So it's going to be four obviously minus 0. It's going to be four minus 0 from the data of course which is going to be four in this case. So my range is four. And if you want to find the mean, you're going to add the third column there, guys. And you're going to multiply the frequency by the number of the points. And you're going to add them up all together, by the way. So, you're going to add 6 + 8 + 10 + 7 + 4. When you do that, you're going to get 35.

[00:22:21]Okay. Now, let's do the number of points times with the frequency. So, let's do it together. So you're going to add the third column to find it out. And then you add them up, you divide them by 35.

[00:22:33]So 6 * 0 is going to be 0. 8 * 1 is going to be 8. 10 * 2 is going to be 20.

[00:22:39]3 * 7 is uh 3 * 7 is going to be 21 and 4 * 4 is going to be 16. And you're going to add them up all together, guys.

[00:22:51]You're going to add them up all together. 0 + 8 + 20 + 21 + 16. Okay.

[00:22:58]And whatever you got here, which is in this case is going to be is going to be 65, you're going to divide it by the the total frequency, which is uh 35. So if you divide by 35, my mean would be would be what would be 1.85714.

[00:23:18]Round it to two decimal places is going to be 80 1.86. That's my mean. So basically you if you want to find the mean in this case it is 1.86.

[00:23:30]If you want to find it you got to add the all the frequencies together to get the 35. You're going to add the third column then and you multiply this by this get zero. 8 * 1 gets 8. 10 * 2 gets 20. 7 * 3 give you 2. 21. 4 * 4 gives you 16. And then you take this total of these and you divide them by the total of the of the of the frequency which is 35. And if you do that it's going to be this is your mean. The range is basically the data subtracted from the highest from the lowest which is going to be here in this case four. My range is four. The mode is obviously two because is the most repeated number because opposing to it is 10. This is how you answer this question. If you want to detail the lesson I told you about it, you can find it on YouTube.

[00:24:18]Okay, let's go. The pie charts pie charts is very important lesson by by the way guys don't you don't have to be fast like me you can pause the video you can write the notes really really important to write the notes here guys so we have 90 meals okay 90 different meals on this pie chart we have pizza we have burgers we have hot dogs we have cakes we have show my wraps okay so look so this is called a circle right and actually uh when we divide the circle in two parts to help us to showcase the data we call that pie chart. So the pie chart is some way some way to represent data like we are using graphs for instance and when you divide the the chart the circle into two equal halves this half is represented as half and half and if you want to show it as a percentage this will be 50% here and 50% there and if you add them together they're going to be 100%. Or if you want to show them as a number is going to be one because half plus half is one.

[00:25:17]Anyways estimating here since this is half. If I do this, this would be quarter quarter quarter quarter which is 25% 25% 25% 25%. And if I showed you this way here, what's it going to be then? So the half will be divided into actually other numbers. So if we have it like this here, the 50 will be divided here for example 25. But if I do this 1 2 3 4, right? And if I add another one here which is 5 1 2 3 4 5. So in this case it's going to be 10% 10% 10% 10% and 10% and so on. Right? So if this is 50%. Uh so how many pizza will we get?

[00:26:00]If this is actually showing this as a percentage uh the pizza would be getting the 50% part right.

[00:26:09]And and yeah and yes. So, um, so the pizza would be getting the 50% pump because it took the half of the circle. As you can see, it's pretty easy. I'm going to use it later on. What about the burgers? What about the hot dog? What about the case? What about shar all together? They add up to 50%.

[00:26:28]So, all of this is a 50%. But what about the burgers itself, hot dogs itself, cakes itself, or shmer wraps itself?

[00:26:36]You're going to what we going to do in this case? You're going to take 50 and divide by four because we have four parts in this 50 four equal parts. When you do that, when you calculate it, it's going to be 12.5% for each. So for 25 12.5% for burgers, 12.5% for hot dogs, 12.5% to cakes, 12.5% to sha wraps. And if you add these up together, they're going to be 50 plus 50 is going to be 100%. Here you go. So now they ask me how many pizza I have 90 meals. These all together they are 90 as a number.

[00:27:13]So I need to extract pizza out of this of Mr. Multiplication. Yes. So pizza is 50%.

[00:27:24]Of what? Of the 90 which is the total meals. 50% can be shown case as 50 over 100 of can be shown as multiplication and 90 right there 0 0 0 5 * 9 is 45 how many guys pizzas do I have 20 45 pizza now the hot dogs hot dogs is 12.5 which is going to be 12.5 over 100 multiply by 90 doing this it is going to be what of the zero with the zero And when you do on your calculator, you can use your calculator totally fine here. 12.5 over 10, you multiply it by 9 then, okay, it would be giving you um 11.25 like hot dogs. Let's say 11 hot dogs, let's say. Okay, 11 hot dogs. And if I got estimated 11 hot dogs, how many burgers? The same thing. It's going to be 11.25 25 burgers because we're going to do the same thing basically. So if you add or if you multiply 11.25 by 4, we're going to give you it's going to give you the rest of it which is the 45 because 45 here 45 meals and 45 parts or pieces of pizza there. Okay, that's it.

[00:28:42]It's really really easy. You can go back to the video and redo it again.

[00:28:47]Basically I divide this is 50% I have four. So each 12.5 each 12.5 if I want to find how many pizza do I have I take the total which is 90 I take of it the 50% which is shown case as 50 over 100 multiply it by the 90 which is the total of meals I have there okay the total of means multiplying do whatever you got to do like I did earlier now let's go the mic is on right please tell me the mic is on okay it's my on so now let's go to the last part which is graphs It's really easy guys using a calculator like I showed you before. Uh so we have here the question says complete the table.

[00:29:27]It's really long blister. What do I do?

[00:29:29]Uh should I like use algebra? You can do that. But we can use our calculator.

[00:29:34]Remember that guys in your IGC is you're allowed to use Excels. You're allowed to use the calculator into two papers uh paper one and paper two. You can you allowed to use the calculator which is a very important skill. But it doesn't mean that you you don't have to show this this the the the steps though. So it's how you have to show the steps.

[00:29:54]Anyways, when it comes to you to complete this table, all you got to do is go to your calculator. Okay, I'm going to try to show it here. Okay, you go to mod. Okay, and you go to something called table. You go to something called table. They will be showcased to you as f ofx. Here f of x is basically y. It's the same as letter y. Our equation was let's do this here. Let's do it like this there. Let's take this. Let's So our equation is 4 y = 4x - 2. So I'm going to write it as you can see here.

[00:30:30]Four uh the letter x. We need to find the letter x here on this calculator.

[00:30:36]Uh it should be the here. So it's going to be alpha bracket to the right which is 4x minus 2. So as you can see to get the letter x here guys you're going to have this to do something. So you press alpha and then after you press alpha you find this closing the bracket to the right and you press it and you're gonna have the letter x and then write minus two as you can see here and then you press equal. G of x you don't have it here in this case. So we press equal again. Uh what's the start? My start here and shown to me in my example is minus2. So I'm going to write minus2. This is my start minus2.

[00:31:17]What's my end? Uh the question is two.

[00:31:22]What's the step? It means how much do I have to get from minus2 to minus one?

[00:31:27]It's going to be obviously + one which is just one. So the step is one equal.

[00:31:31]Here you go. You have my values of x and y's. When the x was minus2, y was - 10.

[00:31:38]When x was minus uh minus1, y was -6.

[00:31:43]When x was zero, y was uh -2.

[00:31:47]When x was uh um 1, y was 2. When x was uh two, y was six. Okay, it's really important to know these guys. Here you go. You have completed this part. The rest of the question will be to draw this. Okay, you will have to write a graph a graph. Okay.

[00:32:12]Um, all right. Let's do it together here.

[00:32:16]So, we're going to have to draw a graph.

[00:32:18]I can see here guys. Okay. Uh, we need to make this to 10.

[00:32:26]So, we do have minus 10 here. Okay.

[00:32:28]Minus 10. So this one this part is going to be long.

[00:32:34]So we have here min - one - 2 - 3 -4 - 5 - 6 - 7 - 8 - 9 - 10. And here what do we have? 1 - 1 - 2 - 3 - 4 - 5 - 6. No. And here we have 1 2 3 5 6 7.

[00:33:05]You have here 1 2 3 4 5 6 7. Now let's draw the point. When x was -2, the y was - 10. So this is basically can be shown as x -2 and y is - 10.

[00:33:23]So let's draw it minus two on the x.

[00:33:26]Here you go. That's -2 on the x and minus 10 on the y.

[00:33:32]Uh which is this one here. Right somewhere here. Yes, this one. So you go down until you reach here because this is this is where they meet.

[00:33:45]Okay. So that's the point I'm going to draw as x. This is minus2 and 10 minus 10 because they meet here together. Uh and remember guys we are forming a line a straight line equation. This is a straight line equation which is y = mx + c. This is my straight line equation. Instead of plus here we have is minus. It's okay. The m value is four and the c value is 2. That's why the line should be uh should be should be intersecting at minus2 on the y- axis which we going to be showing later on.

[00:34:21]Min -1 - 6. This is -1 - 6 here. This is -1. That's - 6. They meet here.

[00:34:29]And what do we have? We have also -1 and - 6. We did that. We have 0 and minus2.

[00:34:36]Zero here, minus two here. So they meet here. Okay. So this is my y intercept which is minus 2. That's why I wrote it here. This is the y intercept anyways.

[00:34:48]And we have one and two. So x1 and 2 y.

[00:34:53]Here you go. They meet here. And we have two and six. Two and six guys. And then you draw your line. Okay? You draw your line like this.

[00:35:06]Okay? That's a straight line equation right there guys. That's it. This is how you draw it. It's very very easy. These are the values. -1 - 6 0 - 2 1 2 6 xy xy xy xy xy and where they meet.

[00:35:31]Now how to how to answer this question guys? It's really important to know how to answer this question. Really really important. Um so we need to find the value of y when we have x as 4 and x is 2 when x is 0 and x - 2 and x - 4. We usually use the calculator like we did here. But uh now we needed to show your substitution how you substitute or the substitute.

[00:35:53]Okay guys substitute here to give the answer.

[00:36:00]All right let's go. which is going to be here y equ= 3 and instead of x guys you're going to write now four so bracket four whenever we replace the letter with a number we put the number in a bracket okay minus what - 3 so I wrote the same equation but I just replace the x with four that's it now since I have a bracket and a number there's multiplication sign between these two it's going to be 12 - 3 12 - 3 guys order of operation multiplication first and then subtraction bit mass is going to be guys 9. So y is going to be 9 when when x is 4 when x is equal to 4. So 4 to 9 that's my point there. Now let's do the same equation but this time we're replacing it with x = to 2. So y equals and it's the three is fixed the x instead of x I'm going to write two this time minus 3. So time times 6 - 3 is going to be three. So y equals to three. But when mister when x is is what is two 2 to 3 let's go to the next one when x is 0. So y = 3 * with 0 - 3. So we have y equ= 2 * 0 0 - 3 is going to be y equaling to -3. So x is going to be equal to 0 uh when y is -3 or vice versa.

[00:37:39]So the same thing y = 3x - 3 this time when x is equal to -2 and then when x = to -4 -4. So let's replace x i y = 3 3 * with -2 - 3. So yeah when you have a coefficient there is multiplication between the letter coefficient. So that's why when I replace the letter with the number I multiply 3 * -2 is - 6 - 3 - 6 - 3 is going to be - 9. Here you go. So x is going to be -2 and y is going to be - 9.

[00:38:17]Uh, y is going to be equal to what?

[00:38:20]Equals to 3, which is x is going to be -4 - 3.

[00:38:25]Um, y is going to be equal to what here? -2.

[00:38:31]Okay. Um, yeah. - 12 - 3 guys is going to be -5.

[00:38:39]So, x is going to be -4 and y is going to be -5.

[00:38:45]I think it is Yeah. Yeah, it's true because when you have negative negative, we add and we put the negative sign. You can pause and go back to the video. Now, the matching question, how to match these with the lines? Know for a fact that y = mx + c.

[00:39:02]This is the gradient, meaning the rise over the run. This is the y intercept where the line intersect at the the the y- axis which is the value going to be there.

[00:39:17]That's it.

[00:39:20]So this one 2x minus one. So basically you have to search uh for a line intersecting at minus1 where x or y on the y ais. So where is it minus one? Oh yeah minus one. Which line intersecting minus one? the line C I don't have to do anything else. So this should be answer as C. So C is my line because it's intersecting at minus1 intersecting at minus1 there as you can see because the value of the y intercept here is minus one. We have this one little one here little guy but I'm going to skip it for now. I'm going to go for this one. y = 2x. What does it mean? I don't have plus c here. Since I don't have it means it's zero. So it's going through the origin zero. This one. And since I don't have a gradient, it means it's one. It's not written. So it's one. What does it mean?

[00:40:12]If I choose this line, which is the red line. If I took a point here and a point there, 1 2 3 4 1 2 3 4. The rise is four and the run is four. And 4 / 4 is going to be 1. That's why we wrote it as one.

[00:40:28]So I'm going to choose D, which is going to be here in this case. As you can see, as you can see in this one, in this way, in this manner.

[00:40:39]So for each one square, I'm going to go up one square. Each one square I'm going to go up one square. Each one square going to up one square. Each one square going up one square. This is going to be my case. So this is going to be D.

[00:40:56]As for this guy here, it's also going through the origin here at zero. But as you can see, it has three. Look. Huh?

[00:41:03]If I choose this for example 1 2 3 and 1. So it's basically 3 over 1 which is three. That's why we have gradient three. So that's it. It's easy.

[00:41:16]So my value is going to be here in this case b leaving the last one which is going through the y at the value of four. So my answer is going to be here in this case a.

[00:41:31]Pretty simple, right? Easy.

[00:41:35]So, uh the question might ask you to do the same thing you did here. Where is it? You did here with the calculator, but it will give you specific numbers.

[00:41:44]The start is going to be here in this question. The start is minus 10 and the end is 10. So, you're going to do it on your calculator. But look at the equation. You're not going to do this in your in your calculator. You're going to do y equal in your calculator, right?

[00:41:57]So, you have to rearrange it. So the question gave it to me as 4x + 2 y = to 1. I'm going to have to make it y equal to something like the calculator.

[00:42:06]Calculator has f ofx and the calculator equals to something which is the same as y. So I have to rearrange it so I can write it properly. So I have first to take the 4x to the other side. It's going to be 2 y = 1. Oh, let's replace the one with minus 4x + 1. Mr. y and minus because 4x to the other side you got going to change up the sign the sign was positive now it's going to be changed to negative I'm not done yet actually I'm going to divide both sides by two this by two and even this by two so it's going to be y equaling to what - 2x + half this is what you're going to write in your calculator guys make sure of that make sure of that so since it's two you're going to divide each term by two make sure of that Guys, you have to pause the video. You have to write down the notes. They're very important. And everything I explained today, I already explained in the class uh during Ramadan, after Ramadan, and never skipped the class without uh teaching you lessons, guys. All right. Anyways, so you're going to do plot this in the calculator. Just do whatever we're going to do like we did earlier.

[00:43:25]So as you can see here, what we did is practically we took the four to the other side. It's going to be minus4 and we divide it by each by two. And after you do that, uh what's wrong with this?

[00:43:42]Okay, now let's go back. f ofx uh what is it?

[00:43:48]Which is basically y - 2 alpha bracket plus fraction bar 1 / what over 2 what's my g of x we don't have to add equal this does actually this time is minus 10 what's the end this time is actually 10 because the question asked me to do that look at the question what's the step I want to have it as one like always here you go each and every time they give you value for y when x is - 10 the y is 41 /2 and here you go.

[00:44:23]Okay, you're going to do it and then you're going to draw it. Okay, it's really important guys. Okay, obviously I'm not going to bring something like this in the exam making difficult in points and decimals. It's going to be way easier. Okay guys, make sure of that.

[00:44:43]Let's try for example, let's for example, let's try.

[00:44:49]All right. Okay. Enough. Enough.

[00:44:52]So, we're going to after we do this, it will be enough. Even like drawing a sketch, it will be enough. Just do the uh the the the calculator thing and everything will be all right. I have covered completely everything that we have been studying for months, guys. So, ultimate revision. It's amazing revision. If you have troubles on something, just write in the comments.

[00:45:14]I'll try to make a separate video explaining explaining it thoroughly or maybe just answering you uh in the comment section. Take care of yourself.

[00:45:25]Muscle act.