In this video we'll learn how to do 2-step problems, which ask us to solve one simple equation, and then take the value we found for the variable and plug it into another expression in order to find the value of the expression.
In this video we'll learn about the special things that happen in the specific instance of a 45-45-90 triangle, which is a triangle whose three interior angles are 45 degrees, 45 degrees, and 90 degrees. This triangle, by definition, is an isosceles triangle, and it's one half of a square, split on the square's diagonal. Show Less
This programme shows students how to construct 60° and 90° angles using a compass and ruler and then how derive 30° and 45° angles by bisecting each of them respectively.
Learn how to determine whether the series converges absolutely or conditionally using the ratio and root tests.
In this video we'll learn about absolute value, and how absolute value is really just distance from the origin on a number line. Therefore, the absolute value of 2 and the absolute value of -2 are the equal, because they're both 2 units from the origin, and therefore the absolute value of both of them is 2. For that reason, we can say that the absolute value of opposites will always be equal. Show Less
In this video we'll learn to find the absolute, relative, and percentage error given by a linear approximation. The absolute error is the distance between the value along the linear approximation, and the actual value of the function. The relative error is the amount of actual error, compared to the actual value of the function. And the percentage error is simply the relative error, turned into a percentage. Show Less
What is a vector space? Even though they are initial taught in the context of arrows in space, or with vectors being lists of numbers, the idea is much more general and far-reaching.
In this video, the teacher demonstrates how to identify the maximum and minimum possible values of a number that has been rounded, and how to identify upper and lower bounds for continuous data.
In this video, the teacher demonstrates how to identify the maximum and minimum possible values of a number that has been rounded, and how to identify upper and lower bounds for discrete data.
This video shows students what adding a constant does to a graph. It shows the result of adding a positive or negative constant inside or outside the brackets of a parabola or cubic graph.
This video shows students how to add or subtract algebraic fractions, by first factorising the numerator and denominator in order to simplify the fractions and find the lowest common denominator.
In this video we learn how to add and subtract fractions with different denominators by finding a common denominator. Finding a common denominator is just about finding the least common multiple of the denominators, and multiplying each denominator by whatever will make that denominator equal to the least common multiple. Show Less
In this video we'll learn how to add and subtract like terms. When we're adding or subtracting, like terms are terms in which both the base and the exponent are the same.
In this video we learn how to add and subtract mixed numbers, which are a combination of whole numbers and fractions. In order to add and subtract the mixed numbers, we'll combine the whole numbers separately from the fractions. In order to combine the fractions, since we're doing addition and subtraction, we'll have to find a common denominator. Then we'll state the final answer as a mixed number. Show Less
In this video we'll learn how to add polynomials together and subtract polynomials from one another. We'll do this by combining like terms, which will be terms with the same base and the same exponent, since we're doing addition and subtraction.
In this video we learn how to add and subtract radicals, or square roots. We can only add together or find the difference of square roots when they are the square roots of the same number.
In this video we learn how to add and subtract rational expressions, which are just fractional expressions in which the numerator and denominator are both polynomials. Just like with simple fractions, we have to find a common denominator in order to add the fractions together or subtract one fraction from another. We'll find a common denominator among the fractions (which will be the lowest common multiple of the denominators), and then combine the fractions. Show Less
In this video we'll learn how to add and subtract signed numbers, or negative numbers. If both numbers have the same sign, then the result will have the same sign as the original numbers. In other words, if we add two positive numbers, the result will be positive. If we add two negative numbers, the result will be negative. If the signs of the numbers are different, then we can subtract the smaller number from the larger number, and the sign of the result is the sign of whichever was the larger of the original numbers. Show Less
In this video we learn how to add mixed measures. Specifically, we learn how to add hours, minutes and seconds, and yards, feet and inches.
Alright, so we've decided to learn all of the maths, but where shall we start? Well, let's start at the beginning. The first kind of math we developed was simple arithmetic. We needed this at the dawn of civilisation to communicate very simple ideas. Most of us can add small numbers together easily, but is there any more we can say about these operations? Let's find out! Show Less
We know about addition and subtraction, we know about fractions, so let's learn to add and subtract fractions! This is now possible because we know how to find the least common multiple of two numbers, which we will need to do to be able to get the denominators to agree. It's easy! Show Less
In this video we'll define adjacent angles and identify adjacent and non-adjacent angles. Adjacent angles must share a vertex and one side, and must not have any of the same interior points.
In this video we'll learn how to solve age word problems using systems of linear equations, or simultaneous equations. Specifically, we know that a man is older than his son, and that the ratio between their ages will be different in some years from now. We need to find their ages today. Show Less
A mobile phone deal and a trip to the cinema are used to explain algebra.