KCET Maths Formulae Revision In One Shot - KCET 2025 Maths🧠📐🔥

Added: 2026-05-05

[00:00:00]So, hello my dear champions. I know you all have been waiting for this particular session, all formula video.

[00:00:06]So, I'll not waste your time. Let's get into the session very very quickly. So, I have included all the major concepts and everything that you need to revise and recollect and have the formula listed at one place for PU1 and PU2 both. There might be some additional information, but I have tried to not exclude anything, okay? At least that much I've tried my best, but my recommendation, please keep the NCERT also with you for some formulas which is not over here, but tried to keep all of it over here anyway, but still keep the NCERT reference also as NCERT summary which is given can also be used for formulas and it is very much relevant for your KCET preparation, right? So, um I'm I have many many you know formulas over here. If you go, I have all these slides and I have all these um to explain as well, but what I will do because certainly I have already done and discussed all the chapters in detail in our you know concept lectures. Okay, we have done and we have covered everything. So, I'll not waste your time. I'll rather give you understanding of how to use this particular formula PDF and simply explain you what you all you can find over here. Once you download the PDF, it'll be very very useful to you. I hope you understand this much, okay? So, let me just show you what I have brought for you. For example, starting with all the chapters you will find uh this is for trigonometry. If you go about this, how do you convert you know degree to radian measure that formula you'll find over here. Then, this is very basic, right? The critical angle formula of sine, cos, tan and others can be formed using what? Reciprocal of sine as cosec, cos as sec and tan reciprocal is cot, okay? I hope you know the trick how to find this result. Uh if not, I'll explain it to you right now. So, for sine, what you can do is very very simple.

[00:01:43]Uh simply over here, write Okay, just give me 1 second, guys. Let me just complete Let me just completely write this one more time for all of you.

[00:01:52]Yeah.

[00:01:53]>> [snorts] >> Just a second. Just a second. Yes, just a second. Okay. So, if I have to write this again, no, it'll be much much easier to understand how to remember these. Even if somebody has a problem in this, let me just help you understand that. How do you write this? So, first I'm going to just write value from here as 0 1 2 3 and 4. Now, divide all these numbers by this letter four, one number four, so not letter. Divide all these by four and take simply root.

[00:02:22]Take root.

[00:02:24]Take root, please. And you'll get the required answer for all these steps. For this, you'll have zero. For this, you'll have 1/4, the root becomes 1/2. For this, you'll have 1/ root two. For this, you'll have what? Uh this value will become root three by two. And this is simply one, okay? Once you have sine, you can just simply write this in reversal form, one over here, this value over here, this value over here, this value goes because sine and cos are complementary in nature and tan is the ratio of sine and cos, so ratio becomes 0/1, 1/2 by root three by two as 1/root three. So, I hope this is clear.

[00:02:57]I know you know this very well, but still somebody might be thinking can there be easier way to understand this?

[00:03:02]That's why I've given you this understanding, okay? Now, continuing, you'll find the um sign convention of all these trigonometric function, sine, cos, tan, cot, sec, and cosec in all the four quadrants, first, second, third, fourth quadrant, which all these are positive and where all it is positive, okay?

[00:03:18]You'll find that. And what is the meaning of the quadrant also mentioned over here? 0 to pi by two is first, pi by two to pi is second, pi to three pi by two is third, and three pi by two to pi is fourth quadrant, okay? So, sine is positive in first and second. Cos is positive in first and the last one, so first and the last one. Tan is first and third. Cot is first and third. Sec is also first and fourth and cosec is also first and second because sine and cosec is reciprocal, right? Okay. So, again, the graphs also I've mentioned over here for sine, cos, and tan, okay? How to draw it? And for inverse, you can learn and draw basically considering this part, considering over here, this part as my one-one function because I have to constrict, right? So, the domain for ITF actually convert this to what? - pi by two to pi by two. If you are drawing this, and the function transforms and you get this as the curve of sine function, right? This is the curve of sine function in inverse form. Sine inverse of x is this, whereas the vertical format, just giving you a reference over here.

[00:04:21]>> [snorts] >> This output value is what? - pi by two to pi by two. And the input value is what? -1 to one. This is just a reference that I've given you for sine function. Basically, to draw inverse of any ITF, just take the image or any any inverse function, just take the image of the original function across which line?

[00:04:40]Across the line y equal to x because any inverse function is what? When x and y interchanges. So, whenever you take the image, whenever you take the image across this line, basically over here, you'll get this as the curve, right?

[00:04:54]You'll get this as the curve what I've drawn over here. This is the curve of sine inverse x. The domain is what? And the domain range also interchanges, okay? Here, what is the domain, sir? Please check.

[00:05:02]The domain is all real number, but we have restricted for ITF, this will be what? - pi by two to pi by two in this case. If I talk about ITF, this will be closed bracket, by the way, guys. This is closed bracket and this is the range.

[00:05:15]In this case, the domain and range interchanges. Domain is what? -1 to one.

[00:05:20]And the range is what? - pi by two to pi by two. Of course, you know that very well because output of our inverse trigonometric function is what? Always an angle, okay? So, range will be always an angle, so that's why this is the value. Same you can find in the graph also. I've given understanding in rough format, but of course, you can find it anywhere. And I've also taught you and when ITF comes, I'll give you the domain and range also. So, as I mentioned for all the functions which is over there, sine, cos, tan, I've given for the major functions, uh the their domain, range, and their repetitive nature, where the period is. So, over here, the period is pi, sir. In the sine, cos, the period was how much? 2 pi, 2 pi, you can find.

[00:05:55]This was >> [snorts] >> 2 pi and 2 pi. All right. So, similarly, if you continue over here, you'll find all the formulas which are involved in sine, okay? Identities also very very important. Please remember all these formulas.

[00:06:07]A few more identities of half angle, double angle, triple angle. So, please remember these. Uh sum and product of sine and cos functions, even tan and cot is also relevant. Uh now, this is your complex number, by the way, guys.

[00:06:21]Complex number. So, you'll find for all the chapters, all the formulas are listed. We know that this is very very useful formula. I power four is one. For the powers of I, when it is multiple of four, it is always equal to one, okay?

[00:06:33]So, you'll find all the formulas listed over here. I am requesting you to download the PDF and go through it, learn all these formulas. If you know these formulas very well, I've given everything that you need, okay?

[00:06:43]Um you know, this is for conjugate. So, everything that you need. For example, uh you Some of you were asking me about the argument of complex number. So, argument is nothing but the angle between your For a complex number, if you draw this line, right? So, if you take this Argand plane, the x-axis represents your real axis and y-axis represents the imaginary axis. So, angle between this This angle is called as your argument, tan inverse of three by two. If you make this, this is three, this is two, sir.

[00:07:10]Then, tan inverse of three by two is called as argument, okay? So, you'll find all the formulas listed over here.

[00:07:15]Please go through it. Please remember these formulas, it will help you a lot, okay? So, for example, again, this is in algebra of limits, okay?

[00:07:23]Um this is very very useful. F plus G question comes, right? Remember? And this is very very important. Sometimes I keep mentioning it using in the question, but never show you the formula, but L'H rule is like this only.

[00:07:34]What is L'H rule? L'Hôpital rule. It works like this. If you're looking to find a function in this format or ratio, whatever it is given, f x by g x or just f x, if you're looking to find the limit of this, differentiate the function under the same limit, limit of the value does not remains, you know, changed, okay? It'll be same value. Standard limit function for polynomial, for sine and tan. Uh this is also very very relevant, okay? And this is in the case where x tends to infinity, what you do?

[00:07:58]You take the highest power common, okay?

[00:08:01]Or divide them and simply apply this condition of limit x one upon x by n, okay?

[00:08:09]Uh when x uh limit x tends to infinity is given equal to zero. I hope it makes sense, guys. Yes? Good. So, again, this is for a special case of uh GIF, greatest integer function, when how can we say that the for any GIF of x, the limit at the integral value does not exist because this is the RHL value for the greatest integer function, this is always one. Whereas, LHL value is what?

[00:08:34]A minus one. And they are Are they equal, sir?

[00:08:36]They're not equal. So, at A positive, it is A. At A negative, it is A minus one.

[00:08:40]So, they are not equal in nature, hence the limit does not exist. So, this is the example on understanding of when and why the limit of greatest integer function on integral values does not exist, okay?

[00:08:53]Some more limits are listed over here.

[00:08:55]So, I hope you download this and go through all these formulas, very very important. Now, all of things over here will be waste for all of you. So, please try to use all of this. Subset conditions are there. Yeah. Uh this is from set theory, guys. This is the case of intervals, both closed, both side open, uh left closed, right open, and right closed, left open, okay? So, this is the different four different cases of intervals that we have, useful in uh linear inequalities, remember?

[00:09:21]Universal set definition, union of set, the operations of set. We have union, uh we have intersection, difference, symmetric difference, all of that is been taken care of over here. You can find all the properties also discussed one by one. So, this was the union definition. Then, this was the properties of union, intersection definition, properties of intersection.

[00:09:39]Disjoint set means nothing in common, [clears throat] okay? So, yeah.

[00:09:42]Difference of sets. We know that what is present in A but not in B. And there's something is which is called as symmetric difference of sets. This is nothing but symmetric difference of sets. In this case, what happens? All which is present in both uh present in either of them but not in both, okay? Present in either but not in both, those are called as your symmetric difference.

[00:10:02]Uh uh so basically elements, okay? Yeah.

[00:10:04]>> [snorts] >> Complement of a set, sir. So, if this is a union set universal universe value and A is part of the universe, then everything but A is called as A complement, right guys? Yes, sorry. This made a mark. Yeah. So, have a look.

[00:10:17]So, everything that you need, De Morgan's law, complement laws, everything has been discussed and taken over here. So, again, this is something which is extra information, but it will be useful for students who are in COMEDK. And this can be useful in CET also for the straight line questions of finding slope, right? So, yeah.

[00:10:32]Straight line chapters are there. How to find the angles? Very very useful, okay guys? So, all these formulas are very important, beta. Please remember these formulas. Please go through these formulas and download the PDF, right?

[00:10:44]I'm not giving you all the formula explanation. It'll take too much of time. It'll be a waste of time. Simply download the PDF and start working on all of these. Everything has been included. Nothing you'll find left to chance. This is important properties of variance, guys. We all know this. Very very important. So, when you add or subtract something to this data, xi represents data, right? xi is the data.

[00:11:03]If you add something to the data, it does not change. Variance remains same.

[00:11:07]Even the standard deviation remains same. If you multiply, then it becomes lambda squared. What happens?

[00:11:13]What happens to the sigma sign in this case? So, sigma dash or new sigma will become what?

[00:11:20]Uh multiplied with lambda means lambda times of old sigma. This is the case of what? Standard deviation. If you add and multiply both, then you can see this change is only in multiplication. So, what happens to the new standard deviation? It'll become simply A times of the old standard deviation. So, change is because of only the product and division, not because of addition or subtraction, okay? When you add or subtract to the data, the variance or the uh standard deviation does not change, okay guys? Very very important. GP you'll find all the formulas over here. AM GM also is there. This is the case of AM.

[00:11:53]This is the case of GM. Very important and high weightage topic from this chapter. Questions have been asked a lot in this particular case, okay? It looks very simple, but very very important, okay? Yeah.

[00:12:04]All right, guys. Infinite terms uh formula is there A upon 1 minus R.

[00:12:08]So, please go through this. As I mentioned, domain and range also I've mentioned over here for all the six inverse trigonometric functions. So, you'll find everything over here, whether it's properties, uh different types of relations, everything has been discussed. This is a case where it is both reflexive identity, but when you add something extra, it is no longer identity relation. Only reflexive is left, okay guys? So, this is equivalence relation. So, many things everything has been discussed over here.

[00:12:31]Uh also, the number of function cases are there. Number of one-on-one function is given by npm, where n represents what? The number of elements in the set B and m is the number of element in the set A. Whenever the n value is more than m, the answer for number of one-on-one function is npm. Okay? What about onto function? Onto function we use either bijections, if it is bijective possible, or we use the mapping. Remember? We map it then 2 power 5 minus 2. Remember those cases. I've solved those those questions over there. So, please check it out, all right? Into functions again, we don't have number of into functions our syllabus, but bijective we have.

[00:13:04]Bijections occurs and possible only when number of bijections if you have n and m equal. Otherwise, what will happen? It becomes zero if n and m are not equal.

[00:13:14]The number of bijection is zero, but number of bijections in when n and m are equal becomes n factorial. All mentioned over here. So, I have written everything. I have discussed everything that you need. For example, my favorite over here, parametric form as you can see.

[00:13:27]>> [snorts] >> Uh if you have function P in terms of F, Q in terms of G. Sorry, P in terms of X, Q in terms of X again. You differentiate P by Q. So, differentiate basically P to Q you're differentiating. You got to differentiate P to X and Q to X and take that ratio. So, properties of log also mentioned over here for someone who, you know, wants to revise once for log all as well. Yeah. Now, second order derivative one question will come from here for sure in your CET. Now, this is very very important as I mentioned. I've given you a summary of all the three type of question that comes. Three questions comes in CET and they'll come one from increasing decreasing, one from rate of change, one from maxima minima. So, I've given a brief introduction for all of this. Increasing decreasing when? When f dash of x is more than or equal to zero, increasing function. Just more than zero, strictly increasing. Less than equal to zero, decreasing function. Just less than zero, strictly decreasing.

[00:14:18]Rate of change when you just write direct derivatives based question. So, when A is pi r squared and you want dA by dR, you get the answer as 2 pi r. But when you use parametric form of chain rule differentiation, for example, A is in terms of pi r squared, you go dA by dT over here. So, you have 2 pi r dR by dT because the variable is changed. It is not r anymore. It is t. So, you got to continue with what in this case? Chain rule. But you have sometime questions of parametric form also, remember? dS by dA. No, dV by dS. Rate of change of volume of a cone with rate of change of surface area of the cone.

[00:14:51]That question was there, no? Yeah.

[00:14:54]Maxima minima local maxima local minima most of the question comes. You find derivative. Derivative if you put it equal to zero, you get x a and b, whatever it is, as a stationary point.

[00:15:02]Sometimes they call it critical point.

[00:15:04]Same thing, okay? When double derivative is less than zero, local maxima. Double derivative is more than zero, then f of a becomes local minima, okay? So, as I mentioned, guys, everything again, this is not the end of it. I have explained it already over here also in the formula format. But just to give you the summary, first derivative test how to find the intervals, okay? Wavy curve method in brief I have given. So, how do you do it? This question was taken as example. Differentiate, you get x as zero your critical point. Plot it over here.

[00:15:33]Positive side over here because coefficient of x is four, sir, which is positive. So, plus and minus. And you simply what you're going to do? You're looking for in this case increasing decreasing both. So, increasing will be the positive side.

[00:15:45]So, positive f dash of x is zero. From where to where? Zero to infinity. So, zero to infinity. When negative, negative infinity to zero. That is the decreasing side. Decreasing side when?

[00:15:54]From here to here. Increasing from zero to infinity, okay? Decreasing from negative infinity to zero. Increasing from zero to infinity. All right, guys?

[00:16:02]Do not worry about it. I know I'm going a little faster, but you can download the PDF and revise all these things, okay? So, I will end again, substitution also given. So, everything that you need has been given over here. All the formulas, integration, everything has been mentioned. Simply download this PDF and revise all the formulas, learn all the formulas. And one more thing before I I know end the session, I would like to show you even in conics also, I have given this result, guys, okay? So, for all the important formula which is there for parabola, ellipse, circles, okay? Whether it is directrix, length of latus rectum, eccentricity, vertex, foci, all the formulas have been mentioned. Please try to remember these formulas, okay? And my recommendation, please match because I have made a lot of things right now. I make I might make a mistake. I'll try not to, but especially for conics, try to use NCERT also to just check everything is right or not. But I think everything is correct only because I have verified everything over here. So, they are they are correct, but since it is exam, I don't want to risk everything for all of you. And this is formulas, right? So, if you get a formula wrong, everything is wrong. So, my recommendation, honest recommendation because I care about all of you, so please use NCERT also together. Yes, you can completely, you know, rely on this, but use NCERT also together just because I want the best for you, okay? So, that's all in this particular class where I talked about all the formulas of maths in KCET, okay? Use this PDF properly and remember all these formulas. I think you'll be good. You can easily score a good amount of marks because you know that many questions in CET are directly formula and concept based. And all of these are covered in this particular PDF and this session, okay? Thank you for listening to me. Uh I will hope to join all of you or to meet all of you in the next class. That's all in this particular session.

[00:17:45]Uh see you in the next class. Take care.

[00:17:46]Bye-bye.