Rational and Non-Rational Numbers
This lesson covers the identification of rational and non-rational numbers. It explains the characteristics of different number sets, including natural numbers, whole numbers, and integers. The lesson also discusses the significance of the number PI in relation to circles.
- 05:41 “All common fractions, whether it's an improper fraction, whether it's a proper fraction, whether it's a mixed fraction, they all fall on that the categories of what rational numbers. Like I said, the proper fraction, the...”
- 06:28 “I have 11 over 20. You could see that 11 smaller compared to 20. I have 17 over 18 at the rest of the others. Now, that is the proper fraction. Now, an improper fraction is the opposite direction, opposite direction in t...”
- 08:00 “the larger volume. So we have percentage. We have fractions. Fractions. Percentage are inside the rational numbers. Take it off. So we have percentage. I said, all percentage are rational numbers. A percentage is a fract...”
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.
- 07:40 “2 in 4 - 2 times -1/2 -2 + 4 in 4 there's 1 times 3 that gives you 3 there. So this go ahead to put B in a better perspective for you. So you can go ahead and sum up your fraction here to have -2 + 3 I give you 1/4 equal...”
- 20:08 “4 times 3 that gives me minus 12 and I know for the fraction is been done by inverting when you have fraction to have fraction what you do is you invert by much implication and that gives me 64 over 9 minus this leads me...”
- 05:08 “It becomes clearer. I remember very well that the value of alpha is actually -1/2 okay. If that is taken you can go ahead and substitute quite well for the value of alpha and for me I can go on substituting for the value...”
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.
- 13:56 “Don't forget this elimination. To eliminate A. Now P plus R equals 1 over 4. 1. 5P plus 2R equals to 2. Equation 1. I have a fraction here. There are two ways to this. I will solve and I want you to follow what you have...”
- 02:43 “So, we're able to solve this very well. You start from equation 2. From equation 2R minus Q over 2 plus 1. In equation 2, I have a fraction. The first step is eliminating your fraction. I'd rather eliminate my fraction h...”
- 09:06 “Okay. Just like the first example, I'm having a fraction here. I can solve it with a fraction. The first step is clear your fraction. So where do we have the fraction? I have the fraction in example. That is equation 1....”
Whole Numbers and Their Properties
This lesson covers whole numbers, including their definition and characteristics. It explains how to express whole numbers and decimal numbers in standard form. The lesson also includes finding prime factors, least common multiples (LCM), and highest common factors (HCF) of numbers.
- 17:03 “it is division. We moved backward. That's out of a 7. So, if you look carefully, so we have, what do I have? I have 7, 7 over how many times do I have? I have 10 ways to power 6. Because of the sign of division, because...”
- 17:50 “and how do I do that? Now, this is 1 over, okay? 1 divided by this. I need to convert this into multiplication. How do I do that? That's the first question. How do I do that? That this one is bit, how do I do that? It be...”
- 18:36 “this is moving up, it becomes a minus. That's negativity. Take notes. It becomes very important. It becomes very important. Now, looking at it again, another example that we have in the part of division. So, you could ha...”
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
- 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....”
- 13:46 “So for this one, I have X minus two over five, okay, and for this one, I have X equals bigger pardon, X plus one, one number one over two. Equal to zero, equal to zero. One more thing I can do before I bring them togethe...”
- 22:35 “Don't forget, the sum and product of quadratic equation is given as x squared minus r for plus beta, bracket plus x, then plus x, I mean, plus alpha beta. So the coefficient of your x squared must always be one. You know...”
Gravitational Force and Fields
The lesson covers the concept of gravitational fields and the laws of gravitational force as proposed by Isaac Newton. It explains the relationship between masses and the distance between them in determining gravitational force.
- 25:13 “now let's get 0.2 times 0.2 give us 0.0.04, now 2.8 points 1 for divided by 0.04 now give us, now give us our fourth is equal to 7.003.5 times 10 raise to the power minus 9,”
- 23:31 “this as F is equal to 6.67 times 10 to the power minus 11 times, this time this we give us 42, 1, 2 we give us 1, 2 over 0.2 or square, now from this side I can take care of this as 1, 2, 2 or this one we are taking off,...”
- 24:19 “here, now let's get this, 6.67 times 42 times 10 raise to the power, let's have this 42 times 6.67 or give us as we have this 28 0.14 times 10 raise to the power minus 9, over”
Trigonometric Ratios
This lesson covers the identification of sine, cosine, and tangent of an acute angle. It explains how to apply these trigonometric ratios to solve problems involving distances and lengths in right-angled triangles. The relationship between the sides and angles of triangles is also discussed.
- 14:14 “that is given, then your hypotenuse. So, I could read, you could know, the particular one to apply. They are designed to cause all the time. Thank you very much. We've come to the end of the class. My name is Oyase Sunda...”
- 11:01 “base this. So I could say my X is equal to I would have 7.14. 7.14 multiplied by tan 35. 7.14 multiplied by tan 35. Now you could take your calculator and press tan 35. You have your answer will give you 4.994. 4.9994. B...”
- 05:55 “over adjacent? Your opposite is what? Your opposite already given to be what? 12. Don't forget. That will give you what? 12. What's your adjacent? 16. So in a simplified fraction. I have three here. Four can go. Successf...”
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.
- 23:10 “So you have minus 2 into bracket 3m plus we have minus 2. So you bracket it out. 5. So minus 2 times 3m is minus 6m. Now you should remember the rules of multiplication, the rules you use in multiplying addition and subt...”
- 20:52 “Like it says here. Multiply 3 by the second term, like I explained earlier, and you get 3b. At the end of the day, you get 6a plus 3b. More examples. You can solve this on your own. I'll just solve just one of it. Expand...”
- 22:23 “10 times b is 10b minus 2 times 3 is 6. 6 times c is 6c, 6c. So we have 2a plus 10b minus 6c. So this is the answer to this. I believe you should be able to solve the rest. I'm just going to go through one more example t...”
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...”
- 15:18 “So A equals 8 over 3. So A is 8 over 3. The question is to determine the rest. So if A is 8 divided by 3, the rest is A plus 1. The first is A plus 1, which is 8 over 3 plus 1. The second is A plus 2, which is 8 over 3 p...”
- 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...”
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
- 11:57 “smaller one, what longest side of the smaller one, that's 9. Because of this point, decimal place, you multiply by 10. So, when you multiply, because of the decimal place, to take it off, you are going to be having 2.5,...”
- 24:32 “smaller one, square, the bigger one is multiplied 4 times the smaller one, but in this proportion, this 4 can say 2 is to power 2, multiplied by water by 96 centimeter square, remember what's okay, as scalar factor is gi...”
- 23:43 “triangle, BAC, that's remember from the scalar, from the scalar that we meant comparison, now you will see why the scalar of 2 can also be checked, so that gives me 384, the bigger one, over 96, now if you look at 96, so...”
Whole Numbers and Prime Factorization
This lesson covers the expression of whole numbers and decimal numbers in standard form. It includes finding prime factors of numbers up to 200, determining the least common multiple (LCM), and finding the highest common factor (HCF). Additionally, it addresses perfect squares and square roots using
- 25:55 “so split them into 2, I have 3 times 5 times 7, for the first part, and the second part, I have 3 times 5 times 7, now splitting them into 2, 3 times 5, that's 15, 15 times 7, that is 1, 0, 5, multiply by 3 times 5, 15,...”
- 09:44 “can two go in this, no, you start off with three, now, three into nine, that gives us what, three, it cannot go in 11, three can still go wrong, three, one, three into 11, cannot go, and the last one is 11, one, one, all...”
- 26:43 “prime factors of this value, 3, 5, 7, it's another prime factor of this value, now the product of the prime factor, what you do in that, these 3, 3 will give this, this gives this, so you pick a 1, so as the product of i...”