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.
- 14:01 “This is where the values or the unknown has a square. That means it has a power of 2, but look at that. We have three identities in what, in quadratic, a plus a square gives a square plus 2 a b. Plus b squared. How does...”
- 12:30 “So that we will have, what we have, 2x squared, good. 2x squared is common to the 3 of them. That gives us an example to be able to factorize them out. Now, the question is, how do you now rewrite them? How? How do you w...”
- 18:53 “It will mean where they are, too. I have 4 less to power 2, 4 times 4, 16. It goes back to 16. 4 square 2 goes back. So, but if it's not a perfect square, then you take it out. But now, it's a perfect square. So it's eas...”
Projectile Motion
This lesson covers the definition of projectile and projectile motion. It explains the concepts of time of flight, maximum height, and range, along with the relevant equations and examples from sports and warfare.
- 13:36 “So by inserting our parameters in this formula, we have U squared U is 200 squared times sin squared theta means the square of the sine of the angle, the angle is 45 degrees. So sin 45, all squared, so we have sin 45 deg...”
- 10:28 “The object has landed. So we now substitute the horizontal. Now, we have R equal to U cos theta horizontal. And times our capital letter T, I hope you remember, 2U sin theta over G times 2U sin theta over over G. So afte...”
- 15:21 “The range, the range, the range, bearing the mind that R equal to U squared sin 2 theta over G, then by inserting the parameters, we have R is 200 squared times sin 2 theta means 2 times the angle of projection, which is...”
Fundamental and Derived Quantities
This lesson covers the definitions of fundamental and derived quantities in physics. It explains how fundamental quantities serve as the base for deriving other quantities and the importance of measurement in physical science.
- 09:28 “We have the acceleration, acceleration is usually changing velocity over time taking and the unit is meter per second squared. The weight of an object is the total of the mass and the acceleration due to gravity. And thi...”
- 10:17 “So this is major in kilogram and this is meter per second squared. So more meter per second squared is equivalent to new thing because we surely discussed this in this subsequent class. At the same time, this new thing w...”
- 22:06 “As established mathematically, the weight of an object is the poorer of mass and the acceleration due to gravity. That is, mass m, mass m times g, which is the acceleration due to gravity. And that is the formula on the...”
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
- 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...”
- 22:46 “384 centimeter square, the first, the second, now if we look at this carefully, we will arrive at the area of the first, area of the second, now how do we compare, remember we said if you are comparing, the bigger one is...”
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.
- 07:10 “Then two is common minus two is common here we have minus two into bracket y minus four equals zero. We can see that one minus four is common between these we have y minus four into y minus two or equals zero. So it mean...”
- 07:57 “can easily say that two raised to power x equals four. Then this is two raised to power x equals two raised to power two. Then since we have the same base therefore x equals two. That is when our y equals four. So when y...”
- 06:18 “two raised to power x or raised to power two. We use what we call the power law yeah. So minus six raised to power two raised to power x plus eight equals zero. So let's why equals two raised to power x. So it means wher...”
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.
- 03:55 “Plus 2 is another term. A term can be a single number, positive or negative, or a variable, one or more numbers and variables that have been multiplied together, terms by terms, and are separated by addition or subtracti...”
- 09:35 “addition operator. It's a plus sign. Without negative, it is positive. So here we have minus four x. And here, the coefficient is minus four, while this is a constant. Another example, if you have three x plus two, this...”
- 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...”