 Maintain a separate notebook for each of the subjects. Maintain a separate notebook for doing the homework as well. And be regular at work. I want you to attempt the homework. Try to understand the difference. And when it comes to attempt, your honesty comes into play. When you say, sir, I attempted all these questions, I didn't get any one of them, I'll be happy. I don't want to see the answers coming up. I want to see you making honest attempts. So first thing is in this exam, be honest with yourself. You're not preparing this exam for anybody, you're preparing this for yourself. It is not even for your parents. Your parents are already well-suited when you do their thing. Your success or your failure will not hamper them. Of course, your success will make a lot of difference to their happiness. But to me also. So you are writing this exam for yourself. Keep reminding yourself every moment when you get delayed at that time. And I am writing this exam for myself. So bridge course, as other teachers would have already apprised you, is basically bridging the gap between your tenth and your eleventh. There are certain tools in maths, in physics and in chemistry, which you would be required to move beforehand. Why? Because multiple teachers would be dealing with you at random. Some teachers would have started chapter X, some teachers would have started chapter Y. And you may be lost in balancing those chapters and you may miss out on certain important ingredients or tools or tricks that you should be knowing in order to handle it. So bridge course in maths would comprise of certain chapters which is not going to be officially taught to you, but you would be expected to use them. The first thing in maths, graph and its transformations. We know maths only in terms of numbers and equations. How many of you have tried solving questions by plotting the graphs? Just in one chapter you had, I think, last year. The chapter. Linear equations, correct? Apart from that, we use graphs to solve the questions very, very rarely, correct? That is not going to work in eleventh and twelfth. If you are clear about the concept, if you want to really save your time solving the problem, you need to take the approach of making graphs. And there is no chapter called graphs in your class eleventh and twelfth. You may have bought your books also for eleventh and twelfth. I will tell you the list of books as well. Apart from the study material that you will be offering. There is no chapter called graphs, unfortunately. But if you turn to a J advance paper or J main paper and see the solutions, you will see a lot of graphs being plotted there. Many of us think this chapter, this way of solving the problem is optional, right? Maths has to be mainly solved by using equations and numbers and formulas. Graph is optional. Sometimes graph may be the only way to solve the problem. And if you are writing J advance, graph can save a lot of time because graph is worth a thousand words, correct? Picture is worth a thousand words, right? I changed it to graph is worth a thousand words, right? Because for you picture is a graph. So if I tell something about a person and I don't show his picture, what kind of boy gets created in your mind? The same boy who is getting created, if I tell you about a function and I don't show its graph to you, correct? The moment you see its graph, you'll be able to assist the characteristic of it. Whether it's even, whether it's odd, whether it's increasing, whether it's decreasing, whether it has corners, whether it is smooth, whether it is break. It has breakage and wear or whether it's continuous throughout. What is the extension of the graph? What is the extension of the graph along y-axis, x-axis? Everything will be very evident once you know the graph. And unfortunately this chapter is not there in your chapter list but used everywhere, correct? So graph is something which I said I thought I would be telling you so that when you start learning math, you have a different perspective about that particular concept. You just don't learn it like figures and numbers. Second thing that you would be immediately required, I think physics has already started with Bexar's, correct? And he would be soon talking in terms of calculus as well. So there will be a session on intro to calculus where I will be telling you what is the concept of limits? What is the concept of differential calculus? What is the concept of integral calculus and what was the rationale behind coming up with a modern day field of math called calculus? I call it as a modern day field of math because older days there was geometry which you learned in class 10. Geometry was very old. Then came the concept of algebra and then came the concept of calculus. So how calculus is going to shape up your math syllabus and of course physics and do a certain exchange chemistry? We will be talking in the calculus. The third chapter is trigonometry which will also overlap with the trigonometry of your class 11. So after finishing these two, when I start trigonometry, I will continue with the flow of your school as well. In your school also probably the first or second chapter would be trigonometry. And as you would all know that we are aligning with your school curriculum. So whatever your school doing, the same thing we will be also doing with you. So you don't have to study multiple chapters at the same time. So what is the expectation from graphs? What do you think will come up in graphs? I think we are having some expectations. So I am going to talk about graphs. What are you going to see in graphs? It's a parabola. 10 to pronounce it incorrectly. It's a parabola. It's a shape which we call as a parabola. Of course parabola. That's why the bridge course is there because here are lot of things which you have never heard before. Functions. What are functions? To give you a simple example. When I write y is equal to x plus 3. What I am doing is I am trying to relate what is x called officially? An independent variable. So normally we call x as an independent variable. x plus 3, you are actually then that picture is called the graph of the solution. Now how would I draw the picture for this? It's not a landscape that I know. Sketch it like this. How do I draw against an x y axis? So what we do is, when we choose an x there is no criteria for choosing it. Hence the name independent was given to it because I can choose it as 0, 1, 10, 100, minus 1, 2.4. But whatever I choose, my y becomes dependent on it. So let's say if I choose x as 1. Can y take any value? No. It will be taking a value of 4. So 1, 4 if you plot, let's say 1, 4 is this point. So 0, 3 points, I get the pictorial representation for this relation. I am not calling as a function right now. I will come to it little later on. So what am I doing? When I am connecting these points or all the points which satisfy this relation, that means I am plotting the graph of it. Understood? So at every point, let's say I take a generic point here x. What are you doing? And y is what? x plus 3. So if you choose your x, y will automatically get dictated by that x that you have chosen. Yes or no? So basically you can say that the picture that you have drawn, the graph that you have drawn is basically a home to two such points which are related to each other. Just like we do it at our home right? Will your dad allow you to stay in his house if you are not related to him? Will you keep me in your house? Of course not. Of course some of you would say yes. But you will never allow a stranger to be living in your house. Correct? Only when you are related you stay in the house. Yes or no? So this, too many people in this house call the graph. Simple analogy for you to understand. Anybody would understand this concept, isn't it? So what is a function then? This is a relation. What makes a relation a function? Now there is a very deep story behind this. I will try to tell you in short because my aim is not to talk about functions in this particular class. My aim is to talk about graphs. But without functions you will never be able to understand what am I doing actually in this class. So just a brief introduction about functions. Now functions are special relations. This is a relation right? It may be a function, it may not be a function. So what makes a relation a function? To understand this let me take you to the next slide. Relations versus functions. Anybody who has taken ad math sensing it, you would know about this. So what is the difference between a relation and a function? I don't want to talk about it. Leave my language, I don't want mathematical jargon. See guys, if you are Einstein, you know Einstein. So he said that if you are equal to explain a concept to somebody in a very simple term, that means you have understood the concept very well. Just a simple language. What is a relation? What is a function? A function can be any sort of graph. A relation can be any sort of graph. A function is meant for the same x value that should not be more than 1 by 5. This is all you know. But you know almost 80% of the things. Just the 20% I will be adding to it. So what is a relation? A relation is a kind of operation which relates two sets. Set A and set B. The set from where you pick your inputs which we call as x or the independent variables, what we call as x. To some element in set B. For example, if you recall, examples which are taken in the previous slide. So let's say set A is a set which is made up of. All of you have seen a set in your past, right? Anybody who has never seen a set before? Let's say set A has 1, 2, 3, 4 as its elements. You all know that in a set, the elements are written only once. In close between flower brackets or curly brackets, whatever you call it. And let's say set B is a set which contains 4, 5, 6, 7, 8. Now what are you doing is? You write the elements of set A in our over shift structure like this. This is called an arrow diagram structure. I will tell you why it's called an arrow diagram. You can see this arrow. So what do we do is? We see that under this relation, which element is mapping to which element of this set? So what is mapping to? So if you put a 1 over here, why should be 4? So we do a mapping of 1 with 4 and we show it by an arrow diagram like this. Anyways, you have to study this in your class 11 chapter called relations and functions. People who are in CVS C4, you would have already done it. Similarly, if I put 2, what is the answer that I am expecting? When I put 2, why should it become 5? So this is an arrow diagram. 3 will give me 6. 4 will give me 7. Now this set A is called the pre-image set. And set B is called the image set. Because when you say you're mapping 1 to 4, 4 is called the image of what? And what is called the pre-image of 4? Understood the naming? These namings you'll come across many a times in maths. That time you should not be like, what is pre-image? What is image? So when you're mapping 1 to 4 under this relation, then 1 will be called the pre-image of 4. 4 will be called the image of 1. Is this nomenclature understood? Correct. The set from which the pre-image is called the pre-image set. The set from which the image is called the image set. Is that fine? So if you have to plot the graph of this particular relation, I am not using the word function as of now. If you have to plot the graph of this relation, what points will you plot on the XY coordinate system? 1, 4, 2, 5, 3, 6, 4, 7 like that. And you will start getting a graphical representation of that relation. Isn't it?