Change of Subject of Formula
This lesson teaches how to change the subject of a formula using the substitution method. It explains the concept of the subject of a formula and provides examples of changing one variable to another. The process involves identifying the current subject and applying inverse operations.
- 00:00 “Hello, I'm Sonday Oyase, I'm your mathematics teacher, but today, and now we're taking an important topic, which is change of the subject of formula, especially substitution. So let's go change of subject of formula, oka...”
- 00:48 “So I'm talking about change of the formula at the end of this topic, what are you expected to know? As expected to know how to change the subject of the formula, how to identify a particular formula and what to do with i...”
- 12:40 “the same. It's on the right hand side, on the left hand side, it is still the subject of the formula because it stands alone. So we'll move to another example, a bit tough one. Now we have example three. This one is made...”
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...”
- 07:31 “with a radical, I put brackets. So the formula is C-A-O-H2 for potassium. Hydrozyde. I believe you understand that example. The next is, how do I name? How do I name compounds? How do I name formulas? When they stand tha...”
- 06:42 “cis, which is 2. Then you write tetra-osophage cis. And the number before on top of potassium, which is 1. Because it's 1, I don't need to put it there. The third one, potassium is 2 plus, potassium 2 plus. Hydrozyde is...”
Changes of Matter and Atomic Structure
The lesson covers the differences between physical and chemical changes in matter. It explains the concepts of atoms and molecules, their arrangements, and introduces atomic number, mass number, and isotopes. The lesson also includes calculations of relative atomic masses.
- 09:58 “ratio, which is 1.82, 1.82, divided by 1.82, and what do you get after doing that? You are going to obtain 3-year ratio, 5-rissue-1. By this you get your empirical formula to C to be carbon-3, hydrogen-5, and nitrogen-1....”
- 11:32 “First, with the empirical formula and your value of n, which are going to determine first, empirical formula times n will be equal to the relatively molecular mass. This is CH2On, equals to the molecular mass, 60, put th...”
- 13:03 “Finally, our molecular formula will simply be C times this 2, H times water times 2, 4, n, o, 2. I believe you understand that, and you can see that from here. The molecular formula is CH2, H4, o2, if you arrange it, you...”
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.
- 08:55 “so it's going to be P minus 30, over changing quantity, under that same P, what is it going to see, 6, okay, so you say, 6, minus 5, 6, minus 5, so your 1 equals to words, equals to P minus 30, over 6 minus 5 equals word...”
- 12:23 “imagine our revenue as well, the same approach, just say to get your q, it's going to be 28, minus words, 28, that's changing CR over changing quantity, okay, and that would give us what, 0, 20 is minus 28, we give us wh...”
- 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...”
Commercial Arithmetic: Profit and Loss
This lesson covers the concepts of profit and loss in commercial arithmetic. Students will learn to identify cost price and selling price, and how to calculate profit or loss these values. The lesson also includes calculating profit or loss in percentage.
- 10:07 “it's still a manipulation of the original formula. If we look for the cost price, being given the profit percentage, is the selling price multiplied by 100 over 100 plus the profit percentage, meaning that we're expresse...”
- 10:59 “That's P. So, either the formula you apply depends on what the question is actually to look for. Pick up the first question, question number two. Esella buys 20 pair of women's sneakers from manufacturer, 20 pair, 10-min...”
- 25:53 “So, you don't ask yourself, "How do I get up the discount from the price?" So, the normal price will be equal to your discounted price, multiplied by 100. All of our 100 minus the discount. They are expected that the dis...”
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
- 21:03 “the first triangle is triangle, triangle, B, A, C, now the formula is 1 over 2 multiplied by base, multiplied by height is the area of each triangle, now that will give us 1 over 2 multiplied by what's the base, the base...”
- 16:54 “is equal to K multiplied by the length of the given shape, the new length you want to get, is equal to K multiplied by the length of the given shape, that means what does that mean, substituting what does that mean, what...”
- 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...”
Gas Laws Overview
This lesson covers the basic gas laws including Boyle's Law and Charles's Law. It explains the relationship between volume, pressure, and temperature of gases, and introduces the Kelvin scale for temperature. The general gas equation PV = nRT is also discussed.
- 05:52 “You're going to obtain V2 equals to V1 T2 all over T1. Then putting the values on the board, you have V1, 1, 2, 5, times T2, 373, all over V, all over T1, which is 290. If you point your calculator very well, you obtain...”
- 16:22 “in simple ratios, one another, and to the volume of the produce, if gaseous, provided at temperature and pressure remains constant. For example, one volume of oxygen is required for the complete combustion of 15 cm cube,...”
- 08:17 “pressure is 2.73 KV. You are asked to find V2. Making V2 the subject of formula from the idea, from general gas equation, you obtain V1, V1, T2 all over T1, P2. And put the values in them, you are going to obtain at the...”
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.
- 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...”
- 22:42 “a, b, c, d, a, and f towards, to high, so we need towards, we need to get the missing figure, how do they get this missing figure, a, b, c towards, to i, how do you calculate it, so without wasting time, let's go to the...”
- 18:32 “the cost, what will be the cost, so remember, let's assume, that's what, you are having on an error, as the worth, as a cost of a bag, and then you know, you quantity you have in the bag is worth, is 20, so for you to kn...”
Introduction to Operations Research
This lesson defines operations research and explains its application in management, industry, and business. It covers the steps involved in solving problems using mathematical models and discusses different types of models used in operations research.
- 09:27 “Your B is when you have your x to 0 and your y is 17 over 4. And your C is when your x is 5 and your y is 3, that is, the point where the first inequality and second equality means. Then D, we have 19 over 2 and we have...”
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.
- 18:29 “Alright, from this place now, we have that what the V square, which is equal to 2G M over R. Now, make V, the subject of the formula, we have the V is equal to the square root of 2G M over R, we give us this, now, let's...”
- 14:22 “Now, I can take care of this and also take care of this. I have it as what's R, which we give us as what's VX square is equal to G M over R. Like I said before, I can substitute the M to be the mass of the X. Then, I'll...”
- 22:42 “actually look for the force, and the force is not given to the force, now let's recall from the formula, which is F is equal to G M1 M2 over R2, now we cannot impute the necessary chain given to R, the G we are giving us...”
Gas Laws
The lesson covers the relationship between volume, temperature, and pressure of gases. It explains Boyle's Law, Charles's Law, and the general gas equation PV = nRT. Students will learn how to perform calculations involving these laws and the importance of using Kelvin for temperature.
- 08:31 “is inversely proportional to its pressure, temperature remaining constant. So using this one we now have a gas occupies a volume of 56 CMQ. P1 is 112 millimeter mercury. V1, 56 CMQ and V1 is what you are looking for. P2...”
- 14:30 “Making V2 the subject of the formula we have, V2 is equal to P1 V1 T2 over P2 T1. V2 is 71800 times V1 17 times T2 to 73 all over P2 101325 times T1 to 9. 110.36 cm cube.”
- 10:21 “you know it is short slow. Using this relationship, V1 over T1 is equal to V2 over T2. V1 equals to 200 centimeter cube, T1 is equal to 75 degree stations for 273 Kelvin. All temperatures converted to Kevin and V2 is 500...”
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.
- 22:40 “then the second root is a collineant beta from the image information given the question you say is alpha squared so for me some becomes alpha plus alpha squared then for me product becomes alpha times alpha squared with...”
- 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...”
- 15:16 “takes me to the real expansion of returns but I still have a thing to do here if I find here or some of this that gives me alpha plus beta everything squared alpha plus beta everything squared I mean alpha beta everythin...”
Measures of Central Tendency
This lesson covers the measures of central tendency, including mean, median, and mode. Students will learn how to calculate these measures using given data sets. The lesson also explains how to handle data with and without frequency.
- 24:14 “all over 2 times 2, and that will give us 6 plus 7.5 minus 7 will give us 0.5. So 0.5 all over 2 times 2, this we can't do this, so we have 6 plus 0.5 and that is 6.5. So therefore our Q3 is 6.5. Now, how to find the 7's...”
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.
- 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...”
- 02:34 “Two X plus Y is equals to four is equation one. Y square plus S is equals to minus 12 is equation two. Now, from equation one, B, the linear equation, make Y the subject of the formula. There, you have Y is equals to fou...”
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.
- 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...”
- 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...”
- 00:02 “Hello. My name is Dorcas Awaye, and today I'll be taking you mathematics. Today we'll be discussing the implication of algebraic expressions. At the end of today's teaching, you should be able to identify and collect lik...”
Work, Energy and Power
This lesson covers the definitions of work, energy, and power. It includes calculations for work done, gravitational potential energy, and power in watts. The lesson also distinguishes between kinetic and potential energy and explains energy transformation and the law of conservation of energy.
- 04:00 “And that is 300 Jews or 300 Newton-Meta. Another example, where we have situations in which a force is applied to a body at an inclined angle theta. The formula will change a little bit. And that would be F multiplied by...”
- 16:03 “Now, in solving this, just like we state the formula, potential energy equals MgH, where M is the mass of the objects. G is associated to gravity and H represents the height to which the object is raised. Now, our M equa...”
- 03:12 “A boy applied a force of 16 Newton to push a wheelbarrow through a distance of 5 m, calculates the work done by the boy. For us to do that, we bring out the parameters provided. The force is 16 Newton and the distance is...”
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.
- 54:31 “now when you have it, that's on that mixed operation, when you have it plus 9, times 15 divided by 15, now don't forget, don't forget that you are going to treat the number in the bracket first, you treat the number in t...”
- 01:05:43 “5 times 0 is 0, 5 times 5 is 25, 5 times 3 is 15, 15 plus 2, you get 17, so you have 17 here, 2 times 0 is 0, 2 times 0 is 0, 2 times 5 is 10, you write 0, you carry 1, then 2 times 3 is 6 plus 1 is 7, so you have 7 here...”
- 01:01:40 “divided by 5 plus 1 over 2, don't forget that this expression in the bracket has been simplified to 70 times of means times, don't forget, of means times times 17 times 17, so now let's simplify it further, 2 goes here 1...”
Oxides of Carbon
This lesson covers the two types of carbon oxides: carbon monoxide and carbon dioxide. It explains their formation, characteristics, and methods of preparation in the laboratory. The lesson also defines the term allotrope and discusses the economic importance of these oxides.
- 07:49 “So, as you can see here, then be collected from this gas jar here, as you can see here. So, now, last quantity of carburetor oxide, all right? is produced by a copy convoxial of carbure compounds like Petru, like we have...”
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.
- 04:44 “minus one. That is four is per minus one. All raised to power was x plus one equals four raised to power two. And by the time we use what we call the power law in our indices, in our law of indices, we can easily have th...”
- 00:45 “when you have an equation of the form, when you have the equation of this form, e raised to power x equals b, then this is what we call Exponential Equation or we call it in this share or in this share equation. So you c...”
Solution and Solubility
This lesson covers the concepts of solution, solute, and solvent. It defines solubility and explains different types of solutions, including saturated, unsaturated, and super saturated solutions. Factors affecting solubility and calculations related to solubility are also discussed.
- 27:44 “molar mass of lead nitrates, now lead is 207, lead is 207, then our nitrogen is 14, oxygen is 16, but the time you carry out all the addition, you know, the mathematics, so you arrive at 331 grams, then number of moles o...”