Let's get to it. So we're still working through this bnandand 14 plus. I know that you've got your Roding entrance exam coming up, so it might be good for us to start mixing it up. We'll make sure to do a little bit of nonverbal reasoning as well by the end of the class, but I would like for us to try to get through the full 14 plus. So we've done all of this. We've done that. So you're very good on that. We've done that. We did this. Nth term needs revision. Let's have a go to this question here. So we've got the bar chart shows information about the weight in millions of tons of bananas produced by each of four countries in 2016. In 2016, China produced 13 million tons of bananas. Draw a bar on the bar chart to show this information. Make get a little bit bigger so that you can really see. Try and be as accurate as you possibly can be. Good. Yep, that looks great to me. Fantastic. Two Marks. Next question. One of these countries produce 6.8 million tons of bananas in 2016. Which country? The Yeah, absolutely. The Philippines is that country that Yeah, good. In 2016, a total of 116 million tons of bananas was produced worldwide. What fraction of the 116 million tons of bananas was produced in India? What is frracking meat fraction, fraction radio bds, I think you do know what a fraction is. A fraction. Is a division expressed like this. That's a fraction. Let tell you what, let me just get you the Chinese translation. This one. So actually. That's a traction. Makes sense. Yes, so like three over five or eleven over 23, these are all fractions. Okay, so one of these countries produced 6.8 million tons of bananas in 2016. Sorry, but a third question. In 2016, in a total of 116 million tons of bananas was produced worldwide. What fraction of the 16 million tons was produced in India? 29 over 116 good, 29 over 116 is absolutely right. And we want to just double check that that's not divisible by anything. 29, I think is a prime number. So the question would be, does it go into 116? Well, no, I don't think it does because 29 times three would end in a six. But that's going to be 60. Oh no, 20, no. Okay, I'm wrong. Actually, you can simplify it. See if you can figure out how to simplify. We're 29 over 116 just enough something. So once you do this in our. We don't want decimals. We don't want decimals in as a fraction. Try dividing both things by 29. That's the way to do it. Yeah. One over four. Good. One over four is correct. Well done. So just be careful of that. Simple, fine, but otherwise, really, really good, really strong. Question 16. Here is six cards. Each has a number on it. We've got three, one, five, five, two, three. First of all, find the median of the cards. What does Median Mean? I forgot going to remember this really important, so. Let's just do a quick recap. So with averages, And I'll just see if I can get you the translations for this. So the mean. Is this this is mean? Do you recognize that word? Yes, okay, so that's mean. Median. Think is this one? Do you recognize that? So it's the idea of that. It's the middle number. So if you have to eleven, 28, 33 and 100 and let's do one more, 205, can you see that? Or actually I just shouldn't do that and know why I did that here. 28 is the median because we've got two numbers on that side and we've got two numbers on that side. It's the middle. It's the middle number. That's all it means. Makes sense, yes. Let's do the two others whilst we're at it. We've got. Mode. And we've got the range to recognize these. Recognize this one. So what does that one mean? Can you try and explain that one? The number that has the most Yeah, good. So let's just do quick examples for each of these. So for the mean, if I ask you, I'm just going to say what is the mean? Of twelve, 18, and 20. Let's do 2021. Good. Just be careful. What's twelve plus 18? 30 was 30 plus 21. Let's theone. 1717, excellence we do 51 divided by three, which is 17 now with the median. You've got to arrange them in order. So I'll do the first one for you. If I say, what is the median of seven, one, three, nine, eleven? What I have to do first of all is arrange them in order. So I'm going to go rather than set seven, one, three, nine, eleven. I'm going to go one, three, seven, nine, eleven. Can you see that, that we're going from the smallest to the biggest? Now I just choose the middle number, which is seven. So it's seven. Sometimes you can also be asked something like, what is the median of, let's say, three, 15 to 19, 21 and 45, let's say. So again, you do the same thing, you order them. So it's starting off with two, then we've got three, then we've got 15, then we've got 19, then we've got 21, then we've got 45. Now here you can see that there is no middle number. The middle is actually between 15 and 19. It's there. Can you see that? We've got three either side. So when you do that, all you have to do is just work out the average of 15 and 19. You can do that really easily by adding 15 and 19 together. 15 plus 19 is going to be 34. 34 divided by two is 17. So again, just to break down what I did there, I did 15 plus 19 divided by two. That tells me what's in the middle of those two, 34 divided by two, which is 17. So if I ask you what is the median. Of nine, one, three, 15, twelve and eleven, what would be the medium of those numbers? Good. Good, excellent, well done. Mode really easy. We'll just knock out a quick example. What is the mode? Of two, eleven, 13, 18, 21, eleven, five, 13, eleven. 1111 well done. Good. And range really easy just means the biggest minus the smallest number. So what is the range of seven, 21, four, five, 20, 41? All I'm doing is I'm picking the biggest number. The biggest number here is 41. Now mining the smallest number which is four and that gives me 37. So biggest number 41 minus the smallest number four and that's it. Really easy. So what is the range of. Two, eleven, 16, 31 and 100. 98, 98, nice and easy. So all of these, you have to learn. You've got to got to got to learn them. The really easy questions. For the most part, it would be a shame to lose out on Marks there. So let's go back to this. They say behind the median, remember what median meant? Median was the second one, the middle. Exactly. So the median of those six numbers. Five Yeah, absolutely five. Well done. Actually, no, it's not. Oh, Yeah. We need to make it in order. Three. It's three good. Okay so Ozma places two extra cards next to the six cards. We don't know what these are. She wants the mean of the numbers on the eight cards to be four and she wants the range of the numbers on the eight cards to be nine. Find the numbers that she should write on the two extra cards. See if you can figure this out. I'm gonna to give you the definitions here on the on the right just so that you don't get confused as to what the question is actually asking. So. Here are the sops, here are the definitions made a little bit smaller. All right. Let's see if you can figure this out. Ten and three. Well done. So we've got definitely the range of the numbers is now nine because ten minus one is nine. Fantastic. And the mean we've got four plus ten that's 14, 16, 19, plus the three would be 22, plus the ten would be 32. 32 divided by eight is indeed cool. Well done. Very well worked out. Good. Well done, Isabella. So next question, we've got a line is drawn on the grid now we've been doing work on this. Hopefully you can figure this out. But perhaps. We need to recap it. Find an equation for l. What is the line equation? Now, just to jog your memory slightly, unless you feel do you feel like you can answer this, Isabella, or have you forgotten how to do this? Maybe I can answer. Good, well done. Go for it. Excellent. Very nice. I forgot a lot. That was perfect. So the the what do you really need? Remember, straight line equations? This is a straight line, right? It doesn't it doesn't curve like this. So straight line equations. Are generally given in the form y is equal to mx plus c, where m is equal to the gradient. Remember, gradient means the slope. So that's what you've just worked out. You've just worked out the gradients. And c is equal to the y axis intercept. So the moment where it crosses the y axis, now what have you figured out? The gradient is here. What does m equal here? Over good, well done. Three over two. And what does c equal here? 11. So what is the line equation? Using this form here. Three over two x plus one, good. And you just miss sed something at the beginning. Y equals very good. That's your equation. Y is equal to three over two x plus one. And you get your two Marks. So again, you can do that. We've learned how to do that. It's just a matter of really revising the topic, making sure that you don't make any any mistakes or you forget something good, really good. So next question, find an equation for the line to l parallel. So sorry, find an equation for the line parallel to l passing through the point zero minus two. Now what does this word parallel mean? Same good. Absolutely. Like this or this or this. Yes, parallel perpendicular is a cross. Parallel like that. Excellent. So parallel to l passing through the point zero minus two. Now, if you want, you can draw this line. Maybe that would help. It's really easy to draw alone because you can just draw l like that and we can drag it to zero minus two. So it's going to look like that. Now what would the equation of that line be? You can see it goes through the point zero minus two like that telling you it does. The equation. Yep, you've got the the last bit right. It's going to look like this. They're asking for the line equation. So again, we're still using this idea here. It's going to be y is equal to bx, plus or minus, blah, blah, blah. Y equals two zero, x equals two minus two. Okay, minus two is correct. This was a disaster. What's the, what's the gradient here? What's the gradient of this line? I equals to three over two. Yeah, three over two. You're missing something. X, there you go, three over two x minus two. So it's a really easy question in a way, because parallel literally means same gradient. That's parallel lines. They have the same radiance, the same slope. So before we even start, we can just write y is equal to three over two x and then we know that the y axis and sepsis minus two. Now notice if we didn't draw, I drew the equation like that. I drew the line equation, which made it easier, but we could still do it. If we didn't draw it, we could go, okay, so y is equal to three over two x because we know it's the same gradient plus c and we don't know what c is. And then we just remember what we did before we were using these points where x is equal to zero and y is equal to minus two. So we go, okay, so I'm going to use those. Y is equal to minus two and x is equal to it's zero. So that's going to be three over to times zero plus c. And then obviously three over two times zero is zero, so I can just write zero plus c minus two minus two z equto c. I get the same option. So whatever way you do it, I don't mind. Some questions are going to be much harder to draw than others. Sometimes they won't even give you a graph. They won't give you a grid. So it isn't important to be able to steait the other way. But that was good. Well done. In spquestion 18. Yeah really, really nicely done and well spotted that you've got a double negative there. So you're absolutely right. That is 18 plus ten, which is to be like really, really strong world. Three Marks. Brilliant. The same thing here. Yes, very good. Well done. Brilliant. Brilliant. Really, really strong on both of those. That was excellent. Three Marks. Okay, solving the simultaneous equations, showing clear algebraic working. We have done this before. Maybe it's been a while. See if you can come to the right answer. If you need help, let me know. Is this two questions or one question? So they're asking, what is x, what is y? Correct. It's an interesting. It's an interesting way of doing it. I don't quite understand what's. No, okay, I see what you mean. No, okay. So the reason that doesn't work, Isabella, is if we just get, okay, if you have two times two x plus y is equal to nine to get rid of that too. Can you see that this this means two times two x plus y, that's what it means. So if you wanted to get the two to the other side, which is not really how you do this question often, you would have to divide by two. So it would be two x plus y is equal to nine over four. Nine over two sorry. You've always got to do the opposite. If it was two plus two x plus y. Is equal to nine, then you can say two x plus y is equal to seven. That's correct. But that's not what we have here. That's two times. So you're always doing the opposites, the opposite of whatever it's connected to. It's connected by multiplication. So we have to divide to get it to the other side. So the way to do this one, remember, is going to what we're going to do is we're going to times the top equation by two. So everything times two in the top equation, equation number one. So what would everything times two give us? X eight x. Four y equals 18 good. And on the bottom, we can keep that as it is x minus four y. Is equal to nine. Now can you see that if we add the two equations together, we're going to get rid of the winds, which is really good for us because we can't solve this equation with an x and A Y. We have to find a way of getting rid of either the x's or the y's before we can solve it. And a simple one like this is probably easiest to do it like this way. So we're adding the two equations together. So starting off with ax plus x, what's that going to give us? A squwhat's atex times x? Is A X squared Yeah. Ax squared, can you understand the difference? Because this is eight times one is eight x times x is x squared. Ax plus x is nine x. Yeah, good. What's four y plus minus four y? Zero. Absolutely right. So plus or minus zero doesn't really matter. And what's 18 plus nine? 27, 27. Excellent. So we've got nine. X is equal to 27. What is x equal to three? Good. So x equals three. Now we just go back. You can choose an equation. Whichever you think is easier doesn't matter. So just choose one of the equations in the question. But now we know what x is, we can figure out what y it's. Equals. And now we're going to figure out what y is. Careful, made a mistake there, so we can spot it. Good. Careful, made a mistake, then. Good. Does that simplify? Excellent, good. And that's our answer, minus three over two. Fantastic. We should find that that works for both of them. So you did the bottom equation. It's always a good idea, I think, just to check that it works for the top. Should we just check that quickly? So if x is equal to three, what does four x equal? Absolutely. And if y is equal to three over two, remember that three over two. This is perfect, by the way. You get full Marks for that. I'm just gonna to do this so that you find it easier to answer. It's also equal to -1.5. So if y is equal to -1.5, what is two y equal to. 1.5 over two. Times two. Two y means two times 1.5 plus two times 1.5. 个富。Was 15 times two. So what's 1.5 times two? There you go. So what's -1.5 times two? Minus three, there we go. So we have twelve. Minus three is equal to nine. It works. So we know that we've got it right. So x is equal to three, y is equal to minus three over two as you wrote to perfect, that's going to get you or three Marks that definitely need to recap that topic. So let's go to question 20. Here is a biased five sided spinner. Kenny spins the spinner once the table gives the probabilities. Remember, we were doing this last time. Probability, the probability of flipping a coin and it landing on heads is one over two. And you can express probability as a fraction or as a decimal as well. So it says Kenny spins the spinner once the table gives the probabilities that the spinner lands on red or blue or on Green. They say, work out the probability that the spinner lands on red or blue. First. Of all red or blue. And if you're struggling with what the question means, let me know and I'll get a ChatGPT translation. Red or blue? Guys. Well done. Excellent. That's your answer. 0.41. Perfect. So for the next one, they say when the spinner is spun once, the probability that the spinner lands on Brown is 0.06 more then the probability that the spinner lands on yellow. So we might want to just start there. I'm going to say ignore the rest of the question to begin with. Let's just start there with that information that they've given us because what this helps us to work out is what is the probability of Brown and what is the probability of yellow? We should be able to use that information to figure it out to see if you can start there and tell me what the probability there for is that it lands on Brown. Oh, yellow. What's the total? Well, you tell me, what is the total. One, one. Thank you. One is all of the possibilities you cut. It can never be more than one because if it's more than one, it's more than certain. It's more than 100% sure. So probability never goes more than one. It can't. Good. Hold on. Was it definitely seven, nine, just double? Check that. Think about this. We want to try to form and solve an equation. We're told the probability that the spinner lands on Brown is 0.06 more than the probability that it lands on yellow. So they both need to add up to 0.26. It's it's dividing the answer. So think of that. What this means is if if you say that this is yellow, for example, it would mean the probability that it lands on yellow is 0.13 and then the probability that it lands on Brown would have to be 0.06 more than that. So that would have to be 0.19. But that does not equal 0.26. They need to add up to 0.26. So if you think about the there you go. Well done. Excellent. Something crazy happened there. Look, why don't you form and solve an equation here? We know that. Let's just write it out. So probability of yellow plus the probability of ground has to equal 0.26, right? You do you agree with that idea? So why don't we call the probability of yellow x? If the probability of yellow is x, what is the probability of Brown in terms of x? Read the question carefully. It says the probability the spinner lands on Brown is 0.06 more then the probability that it lands on yellow. So if the probability of yellow is x, what is the probability of Brown? They. 0.13x no. So we're saying probability of Brown, which is 0.06 more then probability of yellow. What does more than mean if I say what's what's three more than twelve? We eat more than twelve. No. What is it's three plus twelve, three plus twelve, right? So this is saying 0.06 more than yellow. So we've said yellow is x. So what is Brown in terms of x? 0.06x, but that means 0.06 times x. Is that what you mean to mean times? What we'll be doing just a second ago? Plus. Plus. So say it plus, right. Zero points plus x absolutely is equal to 0.26. So now we've got something that we can solve really easily. What's x plus x. Zero point. 0.40. What's x plus x? We've got a okay. I think you're getting slightly confused. Just do this as you would do at regular equation. We've got x plus 0.06, plus x equals 0.26. So simplify. What's x plus x. Zero point, what's x plus x? Isabella, you're making this way too difficult. What's x plus x? Two x thank you. Two x two x plus 0.06 equals 0.26. What do we need to do next? 0.26. Minus. 0.3. Why zero? Where's was 0.13 coming from? I can't see 0.13 anywhere. We're just doing this. Stick to the equation. If you have look, if you have two, x is equal to three plus three is equal to 15. But how would you solve that? This two x equals 15-15 minus three. So what's the difference between this and this? We've got some decimal points in there that's maybe making it more confusing, but there's no difference. It's the same thing. 0.26-0.06, thank you. Good. And what's two x therefore equal to. 0.20 yeabsolutely and what does x therefore equal? Zero. There you go. So we've just worked out the probability of yellow, which was x is 0.1. What's the probability of Brown? 0.16 exactly. Now that can you see that that works? The probability of Brown is 0.06 more and they both add up to 0.26, which is what we wanted. Now we have now all of them add up to give a probability of one. We're going to finish the question just for a sense of satisfaction. Have you got time, Isabella? Have you got two minutes name? So for the sorry, you're starting another class. You're late for class. Okay, let's let's end there and we'll we'll we'll continue next time. All right, Isabella, well done and I'll see you next time. Bye.