Quadratic Equation and Roots
This lesson covers the formation of quadratic equations from given roots. It explains how to find the sum and product of the roots and demonstrates solving for unknown coefficients in a quadratic equation. Examples are provided to illustrate these concepts.
- 16:01 “this gives me alpha squared plus beta squared over alpha plus beta squared minus I can always take care of this because I know the value of my product to be 3 over 8 but I can still relax and fix it later on so in this c...”
- 00:46 “Having said that, we have examples we would like to treat here. Look at the question one here. If you have one of the roots alpha to be -1/2, excuse me, one of the roots is alpha and is -1/2. This question is saying that...”
- 23:29 “48 over 6 and for you know you can get that to be 8 and if alpha cube is going to 8 so therefore your alpha is actually 2 because 2 is the cube of 8 so I mean the cube root of 8 is 2 or 2 is the cube of 8 so if alpha is...”
Roots of Quadratic Equations
The lesson covers the sum and product of the roots of quadratic equations. It explains how to form a quadratic equation given the sum and product of its roots, and states the conditions for equal roots, real roots, and no roots. The lesson also identifies conditions for a line to intersect or be tan
- 23:11 “Thank you for watching. My name is Adidu Kama-Fiz once again. Till next time.”
- 02:30 “plus square root of b squared minus 4a c all over 2a. And let's beta equals minus b minus square root of b squared minus 4a c all over 2a. We can find the sum of these root of equation. We can find the sum of these root...”
- 00:02 “Good day, my name is Adedokun Afeez. I'll be your further maths teacher, and the topic is root of quadratic equation. At the end of the topics, students will be able to know the sum and product of the root of quadratic e...”
Solving Linear and Quadratic Equations
This lesson covers the methods for solving simultaneous linear and quadratic equations using substitution. It explains the definitions of linear and quadratic equations and demonstrates how to manipulate these equations to find solutions.
- 10:43 “If you like, you can make your X the subject of the formula. If you like, you can make your Y the subject of the formula. So from equation two, now from equation two, you make Y the subject of the formula, there you have...”
- 15:30 “X minus two is equals to zero. From here, our S is equals to five or S is equals to two. Since you've gotten the value of X, substitute the value of X into equation three. When X is equals to five, substitute it into equ...”
- 25:41 “to be three of a four, or x is equals to minus two. Substitute the value of x to your quadratic equation three. Then you get your value of y to be 27 over four, or 6 over number three over four. Also, when you are solvin...”
Polynomials and Their Properties
This lesson covers the definition of polynomials and their degrees. It explains how to divide a polynomial by another polynomial of lesser degree and introduces the remainder theorem. Additionally, it discusses how to find factors of polynomials and solve cubic equations using their roots.
- 00:00 “Good day. My name is Adedokun Afeez. I will be taking you furthermath and the topic is Polynomials. At the end of the topic, students will be able to know how to define Polynomials. Define a polinomia by a polinomia of l...”
- 12:19 “equals 0. So, this is going to be what is common x is common. So, x minus 3 what is common minus 3 is common we are going to have x minus 3 as well equals 0. So, we're going to have we're going to have this is plus. So,...”
- 24:41 “one is divide Puy-Numia P1 of x equals 2 x squared equals 2 x squared minus 3 x plus 9 by P of 2, P 2 of x equals x plus 3. We have to use lung division method. And find the remainder when x is equal to 3 plus 5 x square...”
Roots of Quadratic Equations
This lesson covers how to find the sum and product of the roots of a quadratic equation. It also explains how to form a quadratic equation given the roots and states the conditions for equal roots, real roots, and no roots. Additionally, it discusses the relationship between a line and a curve in te
- 24:13 “that gives me x squared minus alpha plus beta x plus alpha beta equals zero. When I have this, quickly I can now see what to do with this. That means my sum is equal to minus alpha plus beta equals to minus one over thre...”
- 23:24 “so that you don't deal with like numbers. So that gives me x squared, two over six could lead me to minus one over three. So I have x over three, all right? And 20 over six could lead me to 10 over three, and that would...”
- 15:18 “you can just make it three X over two, and you now go for minus two of five times X, that gives you minus two X over five. And the last one minus two of five times three over two, that gives you minus, okay, six over 10....”
Change of Subject of Formula
This lesson teaches how to change the subject of a formula using the substitution method. It explains the concept of the subject of a formula and provides examples of changing one variable to another. The process involves identifying the current subject and applying inverse operations.
- 26:03 “the formula. Now, with this, we start from A down to the next one to the next to the next and now this. So, you could also pick it to this side and take it to this side. In another side, you decide to put it. There is no...”
- 12:40 “the same. It's on the right hand side, on the left hand side, it is still the subject of the formula because it stands alone. So we'll move to another example, a bit tough one. Now we have example three. This one is made...”
- 22:37 “square. Now, I am introducing square, someone said, oh, but those ones we are not square yes, you could have a system of equation, you could have square, you could have square root, you could have Q, you could have Q, so...”
Solving Simultaneous Linear Equations
This lesson covers how to solve simultaneous linear equations using substitution and elimination methods. It also explains how to identify linear equations and includes examples for practice.
- 09:57 “They want to make the stability of the formula. What we're careful? Always go for the one that is linear. Or a variable that has no coefficient that is greater than 1. I have 3y, the coefficient is 3. The coefficient of...”
- 08:13 “Q equals to 2. I have y minus x over 4 equals to 3 and 3y plus x equals to 23. That's what I want to solve. I will solve this. y minus x over 4 equals to 3. Equation 1. I want it to be the second equation. The seventh eq...”
- 10:45 “You take this to the other side. And I will become 23 minus 3y. Not that I have this. I can substitute now. Going back to this equation that I have here. Equation 3. I have 4y minus x equals to 12. And I have x equals to...”
Factorization of Algebraic Expressions
This lesson covers the factorization of simple algebraic expressions and quadratic expressions. It includes methods for identifying factors and solving related word problems.
- 10:58 “Multiply by x multiplied by x. I have what? 18. I have 18 x with to power 3. That means there are 3 x. Now, what are the possible values? I have 2 multiplied by 3 multiplied by another 3. Now, how many x do we have? 3 x...”
- 16:34 “the perfect square. So with that, I will give you a exercise to do the expansion. That's opening of bracket for the second and for the third. So I've been able to open the bracket, this means they are 2. So a minus b, a...”
- 11:43 “Taking it out, what's common in the 3 process? In the 3 process, if you are very observant, you will see 2, 2 connecting to this and 2 connecting to this. They make it more easier. You will see an x, yeah, connecting to...”
Simplification of Algebraic Expressions
This lesson covers the definition of algebraic expressions and their components, including terms and coefficients. It explains how to identify like terms, perform arithmetic operations on similar terms, and simplify expressions by inserting or removing brackets.
- 00:02 “Hello. My name is Dorcas Awaye, and today I'll be taking you mathematics. Today we'll be discussing the implication of algebraic expressions. At the end of today's teaching, you should be able to identify and collect lik...”
- 10:21 “So we can easily note which ones are the coefficients. For the variable x, the coefficient is three. For variable y, the coefficient here is plus five. And then we have constant of minus nine. x and y are the variables a...”
- 12:46 “The same thing applies to the second example. The second question, 10 minus x plus two y. So looking at this, the coefficient of y is plus two. The coefficient of x is one. There's an invisible one here. You don't just h...”
Similar Shapes
This lesson covers the identification of similar shapes such as triangles, rectangles, squares, cubes, and cuboids. It explains the criteria for similarity, including proportional sides and equal angles. The lesson also includes methods for enlarging figures using scale factors and calculating lengt
- 32:36 “Calculate the area of one phase of cube K, area that is the area of the cube. Then calculate the volume of cube K. You calculate the volume of cube K. Thank you very much, I come to the end of the class. My name is Oyase...”
Translating Word Problems into Equations
The lesson teaches how to translate word sentences into mathematical equations. It covers the use of variables to represent numbers and how to express word problems as algebraic expressions. Students will learn to solve simple equations and check their answers.
- 14:30 “And you may not use inverse operation. Let me teach you this. You can't go like this. Once you have something like this, you want to always find a way to make the one with a variable alone on one of the sides, making it...”
- 13:44 “And the first of the three numbers is A, as it is C in A, determine the rest. These are the rest, but what is the value? That is what we want to get now. Because we can get the value. See, let's see if we can get the val...”
- 19:25 “We've come to the end of today's class. Thank you so much for watching. My name is Dorkas Aoye, till next time.”
Determinants of Matrices
This lesson covers how to find the determinant of a 2x2 matrix using cross multiplication. It also explains the determinant of a 3x3 matrix using Kramer's rule and the co-factor technique.
- 17:39 “of matrix 2 by 2. Okay, so that is following the process. So, we can also apply the same process in solving 3 by 3 matrix. But, however, you need to also look for the co-factors of the matrix as shown. So, we can also ap...”
- 19:18 “as, with respect to the variables. That is a coefficient. So, what we have is, we have this, take the coefficient, we have 2, 1, 3. We have 3 minus 4, 1. And we have a minus 4, we have 5, we have minus 2. Then the variab...”
Graphical Method of Simultaneous Linear Equations
This lesson teaches how to solve simultaneous linear equations using the graphical method. Students will learn to create a table of values, plot the equations on a graph, and identify the point of intersection as the solution. The focus is on using the x and y axes correctly.
- 12:11 “x equal to 2. Sorry, x equal to 2. If I would come to 3, x equal to 2. So, I have 2 minus 3. Now, give me, negative is still on the high side. That's minus 1. Now, I have the next one, where I have x equal to 3, x equal...”
- 21:26 “Sondi. Thank you.”
- 11:26 “Now, my x, this is it. So, substitute it in, I substitute when x equal to 1, when x equal to 1, x equal to 1. I will have y equal to minus, y equal to, we have 1 minus 3, 1 minus 3. Remember, negative all positive down,...”
Gas Laws Overview
This lesson covers the basic gas laws including Boyle's Law and Charles's Law. It explains the relationship between volume, pressure, and temperature of gases, and introduces the Kelvin scale for temperature. The general gas equation PV = nRT is also discussed.
- 05:52 “You're going to obtain V2 equals to V1 T2 all over T1. Then putting the values on the board, you have V1, 1, 2, 5, times T2, 373, all over V, all over T1, which is 290. If you point your calculator very well, you obtain...”
- 17:08 “And if we try the question, you are comparing 18 and oxygen, and from the balanced equation, you have two volume of 18 to react with seven volume of oxygen. And you are asked that what volume of oxygen, what volume of ox...”
- 11:26 “understand the next examples. Since 1.5 more of an ideal gas at the temperature of minus 15 degrees Celsius, and pressure of 2 atmosphere, what volume in DM cube really gas occupies at that temperature? Given the value o...”
Exponential Equations
This lesson covers the definition and properties of exponential equations. It explains how to solve exponential equations of linear form by ensuring the bases are the same. Examples are provided to illustrate the process of finding the unknown variable in these equations.
- 05:30 “with this we have minus x minus one equals two. And this would be minus x, we collect the like times, we have minus x equals two plus one. Our minus one will be called plus where we transfer this to the other side. So we...”
- 08:56 “of linear of quadratic form. And that of x or x is number two is for exponential equation of a linear form. So therefore we can use this the method that we use in our previous examples to solve this as a size. So thanks...”