Heat and Temperature
This lesson covers the definitions of heat and temperature, their differences, and the effects of heat on substances. It explains the kinetic molecular theory and how heat causes changes in state, such as solid to liquid and liquid to gas.
- 08:39 “Then, earlier expansion, increasing length and breadth. And we talk about volume expansion. That is increasing length, breadth and height. Examples of tamar expansion are stock lid of a glass jar. Normally, when we have...”
- 15:00 “That's what we have in our refrigerator, fridge and some other instruments. Now, linear expansion. When substances are heated, there are expansion varies from one substance to another. For solid, there is always an incre...”
- 07:51 “Tamar expansivity or tamar expansion is the tendency of matter to change its shape. Earlier, volume and density in response to change in temperature. In other words, when substances are subjected to heat, there is every...”
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.
- 13:29 “minus 1 over beta so where you get that all you do is expand and expanding is quite easy you know the first term here goes to multiply this and this goes to multiply this in the same way you multiply this by this and in...”
- 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...”
- 14:22 “squared I can do a good thing to rearrange so I can come up with a good thing and that is pull this first and the last together and the middle one together so when I do that I can have 1 over alpha squared plus 1 over be...”
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.
- 19:12 “plus 4 times 2. In other words, 4 groups of 3 plus 2 is the same as 4 groups of 3 plus 4 groups of 2. For example, we expand this expression. 3 into brackets 2a plus b. Now with expansion and the distributive law, this i...”
- 17:36 “So this can be regarded as a term on its own, which is the same thing as 2 times a plus b. It is also the same thing as a plus b plus a plus b, which is a plus b plus a plus b. The same as, then you rearrange. Like we di...”
- 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...”
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
- 02:27 “When I have this, I can expand. And when I just done, what happened is, you have to follow the process we had before. The X here can go to multiply the X here, and the X here can go to multiply this. In the same thing, t...”
- 11:22 “that means I'm gonna have X minus five into X plus four equals zero. So when I have that, what comes out is this. In the same vein, I can expand. You can just write for your teacher to know, expand. So your teacher will...”
- 14:33 “and put it together, that is, you have X minus two over five, two over five, okay, into X plus three over two. All right. Well, with this, you can as well expand and come out neatly, that gives you X squared for X times...”
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.
- 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...”
- 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...”
- 16:13 “cost 20 more. So noodles is X plus 20. What are the cost of 4 such as of milk and 8 such as of noodles? So for 4 such as of milk, 4 such as of milk, that's 4, say 4 milk, 4 milk such as X and 4 places, X in 4 places, whi...”