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.
- 11:53 “go ahead to know what my sum what my sum will be and what my product will be. So with this I have alpha plus beta squared this gives me alpha squared plus 2 alpha beta plus beta squared all over alpha beta squared yes it...”
- 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...”
- 03:21 “When it is done you can now start to see how this comes out. It is caught off here so this gives me my sum and this gives you my product and I can easily fix it. I have for you alpha+bx that is sum is equivalent to alpha...”
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
- 04:47 “So this now leads you to what we have. We can write out exactly what the sum and product of quadratic equation will be. In my mind, if I recall very well, I remember that the equation of X is one, okay? Then the equation...”
- 05:39 “Okay, and the last one, alpha beta, that goes for my product. So what we do here is that given the two roots alpha beta, you have to establish that the sum could be given us minus alpha plus beta and the product could be...”
- 21:45 “If you rewrite this, that gives you six x squared, as in the two x now comes to the left hand side to give you minus two x, equal to the 20 comes to the left hand side to give you minus 20 equals zero. All right, a good...”
Cost of Production
This lesson covers the concept of cost in economics, focusing on the cost of production. It explains different types of costs, such as fixed and variable costs, and discusses the factors of production that contribute to overall costs.
- 26:47 “marginal, you have to use your total cost, 18 minus 14, now give us what, four, okay, you don't need to start burdening yourself with this, because when you say two minus one, three minus two, four minus three, you still...”
- 25:58 “okay, over changing quantity, anything marginal, the first line is always dash, you can see, here, for the first unit is dash, so you start from the second one, very easy, even without capital it or you can do this, just...”
- 02:24 “of yeast, you need to consider the cost of butter, all these are words are cost that must be words considered before you can have the words the overall finished products. So the actual amount you have spent, the value th...”
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.
- 07:04 “could find out what the exact age is. But as it is now, there's no value. We leave it the way it is. Second example, a shop owner sells maize at Sunera Parkop. She also sells rice Parkop at double the price of the maize....”
- 08:41 “I would have written Y-Nera here. And then if she sells a cup of rice as double the price of maize, that would be two Y, which is the same thing as two times Y. So two times two. So she sells a cup of rice at four Nera....”
- 17:01 “You can just say 4 X, so you can say X plus X plus X plus X. This is a cost of 4 such as of milk. And 8 such as of noodles, 8 noodles would be since noodles is X plus 20. So you have 8 times of X plus 20. So 4 such as of...”
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.
- 25:31 “is the next one, or division. In the expression, you do multiplication next. So you use the distributive law to multiply the brackets by its coefficient. Remember that 4 times 3x means 4 times 3 times x. 16x plus 2 plus...”
- 04:44 “you're lent to hard or subtract objects, you lent that, for example, one apple plus one apple plus one apple plus one apple can be written as four apples. That is one apple, one apple plus another one. Let me represent i...”
- 07:10 “Two multiplied by c. That is what it means. So the following expressions using a simple annotation. Y plus y plus y plus y. Instead of writing all of that, you just have five y. The same thing with 8 times b gives you 8...”
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.
- 15:44 “Now, what do I do next? Open the bracket. Remember, multiplication comes. A times a gives me a square plus a times b gives me a and b. And plus times plus, I have it as addition. b times b gives me b square because they...”
- 07:05 “Like 2 multiplied by 3 multiplied by a square, that means a is 2. By a multiplied by a multiplied by a b. Now, we go for the second one, that's 15. I have 15. What are the possible factors of 15? I know the ba is the squ...”
- 26:52 “Factorized, P square minus 10P plus 25. The last one says factorized, x square plus xy plus 8x plus y plus 8y plus y plus 8y. So, you could see that I had to bring it into four. So, you could group it into two, two, two....”
Revenue Types
This lesson defines revenue and explains its three main types: total revenue, average revenue, and marginal revenue. It covers how to calculate each type and their relationships to production and sales.
- 18:06 “So that's where you have the maximum profit. Okay? So profit is maximized as output for. That's how you tell them. Profit is maximized as what? As output for. Then let's go to some things. Calculate the profit when quant...”
- 01:01 “However, when you produce an item and then you sell that item, you will realize money. Is that so? Now, the total amount you have realized when you sell a commodity you have produced, that total amount realized is what w...”
- 05:10 “So, let's get the words, the solution to these words, so this interesting question won't have to the other. Look at the board, here you have what, P is on the wall, it's first on the CR, remember the formula I give to us...”
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,...”
- 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...”
- 23:12 “to give the product, express 1025 as a product of its prime factor, express 1025 as a product of its prime factor, now how do you do this, carefully look at it carefully, you have one cell, use the division method, by no...”
Chemical Symbols and Formulae
The lesson covers the symbols of the first 20 elements and how to write chemical formulae and equations. It explains the differences between elements, compounds, and mixtures, as well as the concept of radicals and valency. The laws of conservation of mass and constant composition are also discussed
- 09:08 “for ordinary compounds, the summation is zero. 2 times 1, 2 plus 4. 4 times minus 2 is minus 8, equals to zero. Sofor take our collect-like terms, take the numbers to the other side minus 8 to the other side of the compo...”
- 14:44 “that nitrogen with balance, nitrogen with balance A. My hydrogen is balanced, my nitrogen is balanced. The next I need to balance is oxygen. How many oxygen do I have now on the product side? I have 3 A, 2 A, making 5 ox...”
- 15:36 “4 N O, nitrogen 2 Z. Then you have 2 times this to give us 6 water. With this, you can check whether your equation is balanced or not by doing atom count. On the return side, on the return side, my nitrogen, my hydrogen,...”
Multiplication in Binary Numbers
This lesson covers the multiplication of 2-digit and 3-digit binary numbers. It explains the basic rules of binary multiplication and how to apply them in calculations. Students will learn to perform binary multiplication without borrowing.
- 16:32 “four one one multiply by one zero one evaluate one zero zero one one multiply by one one one thanks for watching my name is Oyase Sonde till next time”
- 15:40 “transferred to this place so that gives us plus one yeah plus one one plus one that's two we turn back here that gives us zero that what do I have then I have the last one transferred yeah that's plus one so plus one plu...”
- 06:09 “which is called the one. So, let the one goes now. One time this. You remember, you have started, you have left 2. So, you're starting, you've left 2 first to start from the third, you get it. So, you've left 2, you're s...”