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.
- 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...”
- 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...”
- 12:17 “Now X square plus X square is equals to two X square minus seven X minus seven X to give you minus 14 X. This is 49, which is plus. If you break 29 because you want to equate everything to zero, plus 29 when you cross eq...”
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.
- 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...”
- 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...”
- 23:16 “And have your P to be 5. And likewise, you can check to know if you are right or not. Evaluation. Using some decision method, solve the following PS of simultaneous equations. 4x minus y equals to 4. It x minus y equals...”
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...”
- 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...”
- 03:10 “in the form of two raised to power x. So we have two raised to power x equals two raised to power five. Two raised to power five will give us 32. So we have, and you can see that we have the same base. Since we have the...”
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.
- 26:02 “minus 28 x plus 12 is equal to 0 and also number two if you are given an equation to x squared plus x minus 12 is equal to 0 you need to find the value of 1 over alpha plus 1 over everything squared thank you for watchin...”
- 18:31 “that my alpha beta is actually 3 over 8 so I have minus 2 over 3 over 8 so with this in view I can go ahead and find the result at the value of my 1 minus alpha 1 minus I mean 1 over alpha minus 1 over beta so here I go...”
- 25:12 “what is going to be the value of k therefore k over 6 is equal to 6 and therefore k is equal to 36 so with this you have come to realize that k is 36 when the roots are 2 and 4 so with this you have been taught how to ge...”
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...”
- 25:05 “Is equal to minus 10 over three. So you can try this one with the subsequent one. And in order to one of this session, I'll leave it with this information. Questions one, form a quadratic equation, whose roots are minus...”
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.”
Addition and Subtraction of Fractions
This lesson covers how to add and subtract fractions with the same and different denominators. It explains finding the least common multiple (LCM) to create equivalent fractions for addition and subtraction. Examples are provided for practice.
- 02:27 “So we have ten over 35 plus seven over 35, giving you 17 over 35. Can you try this? Five over eight plus one, divided by six. You can try that out. The correct answer is 19 over 24. Now example one, simplify five over si...”
- 06:39 “12 times 6, we give you, only give you 12 times 6, 72, plus 5, 77. So we have 77 over 12, minus 3 times 4, 12, 12 plus 3, 15, we have 15 over 4. So with this now, we solve each as I have done the one above. So how do we...”
- 07:28 “the denominator by 3 to get to f. It also means that you're multiplying the numerator also by 3. Giving you 45 over 12. So for us to solve this problem now, 77 over 12, minus 45 over 12, that will give you 32 over 12. So...”
Linear Inequalities in One Variable
This lesson covers linear inequalities in one variable. It includes identifying, solving, and representing solutions of linear inequalities on a number line. Word problems involving linear inequalities are also addressed.
- 10:05 “what, minus 25, as my answer, so to check for my solution, what do I simply need to do, I just simply need to pick this value, substitute it into the equation, then I can always check for it, now, look at that, move to q...”
Basic Operations on Whole Numbers
This lesson covers addition and subtraction of whole numbers, including how to align numbers by their place values. It also explains multiplication and division by 10, 100, and 1000, and introduces the use of the BODMAS rule for solving mixed operations.
- 41:36 “you'll put 6, 275 in the square root sign, then you have 5 written outside, I want to use the long division method now. So, now, 5 in 6 is 1, you write the answer here, 1, 5 in 6 is 1, so 1 times 5, 1 times 5 is 5, you w...”
- 01:03:30 “oh, because multiplication comes first, come before additional expression 5 times 2 is 10, you do 5 times 2 is 10 plus 35, now the final answer will be 15 minus 10 is 5 plus 35, 5 plus 35 is 40, so our answer is 40, so m...”
- 05:18 “They have four, three, two, make sure that unit column is in line, look at the number seven and two are on unit line, three and three down, tens line. So make sure that you arrange them correctly so that you don't make m...”
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.
- 13:33 “Why? Because they contain the same variables, which is p. We can also add 3x plus 4x. Because both terms have the variable x. We can combine the terms using the operation that is given, which is in this case, the additio...”
- 16:03 “8x plus the tin y minus x minus 4y. Just as I did earlier, you rearrange, gathering those ones with x together, 8x minus x plus 13y minus 4y. So 8x minus x. 8x is minus 1x. Remember, there's an invisible one. So you have...”
- 14:21 “So I'll just stop this now. 2x plus 3y plus 5x plus 2y. How do you solve this? The first thing you do is to rearrange. In such a way, where some variables are together and the others are on the other side, this way. So s...”
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.
- 07:23 “the equation, the equation is y equal to minus x plus 5. So, when x equal to 1, the y equal to 1 minus 1 plus 5. So, minus 1 plus 5, that gives us 4. Why is it 4? Remember I said, negative down positive or your final ans...”
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.
- 18:06 “So if these are in a perfect square, it's easy, very easy. So you put it in square and you express this how, how do you break it out? So someone says, oh, it becomes simpler. So I have a solution to the problem. Now, thi...”
- 26:04 “It would be twice the number of girls, so that would be 120 times two. So, 120 times two, that would give us 240. So, when you had 240 plus 120, it would give you 360, total number of students in the school. What problem...”
- 25:15 “From the extra. Now, what are the number of boys? We have it as two, two X plus what's the number of girls? We have it as what? X. Equal to 360. So, I have two X plus X. Remember? That gives me word, three X equal to 360...”
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
- 25:22 “these 2, if it cannot be in this form then your answer is wrong, now the last part is applying it to water problem, how do we apply it to water problem, how using your scalar factor to solve a problem, olatical wants to...”