This video discusses the concept of natural numbers, whole numbers, and integers, and how they can be represented on a number line. It explains how addition and subtraction of these numbers can be represented on the number line, and how the inclusion of negative numbers (integers) allows for the representation of all possible results of addition and subtraction. The video also touches on the historical acceptance of negative numbers and how they can be applied to real-world concepts such as bank accounts and net worth.

In this video, we discuss the concept of rational numbers, which are numbers that can be expressed as a fraction with a numerator and denominators that are both integers. Then we explain how to add and subtract rational numbers, and how to find rational numbers between two fractions. The video also fleetingly mentions the concept of irrational numbers, which are numbers that cannot be expressed as a fraction.

This video explains how the decimal number system works, how fractions can be converted to decimals, and how some fractions can be represented with a finite number of digits while others cannot.

This video explains how to convert a terminating decimal number into a fraction. It discusses how to shift the digits in a decimal number by multiplying it by 10 and how to simplify the resulting fraction.

In this video, we will learn how to convert repeating decimal numbers into fractions, explore different methods for eliminating repeating digits, and use examples to illustrate the process. We will also discuss how to handle fractions with non-integer numerators and denominators and provide motivation for the use of irrational numbers.

In this video, we explore the concept of irrational numbers, which are numbers that cannot be represented as a ratio of two integers. We examine the proof of the existence of irrational numbers, which involves demonstrating that the square root of two cannot be represented as a fraction. We also look at the characteristics of irrational numbers, including the fact that they cannot be expressed as terminating or repeating decimal numbers and that there are an infinite number of them.

"Join us in this video as we explore how to plot irrational numbers on a number line. Using the spiral of Theodorus, we'll learn how to visualize irrational numbers as the hypotenuse of right-angled triangles and use this technique to plot roots of natural numbers like root 2, root 3, root 4, and more.

Exponentiation is the shorthand for repeated multiplication, where a number "a" raised to the nth power is the same as multiplying n a's together. The video explains how to combine exponential expressions through operations such as addition, subtraction, multiplication, and division. It also covers the meanings of exponents of zero, one, and negative numbers.

This video discusses the concept of exponentiation and how it can be applied to expressions containing multiple terms, including those with exponents. It explains that raising a product or quotients of terms to a power is equivalent to multiplying the exponent of each term in the expression by the power to which the entire expression is raised.

This video describes the concept of rational exponents and how they can be used to represent the roots of numbers. It explains that an exponent of one over n represents the nth root of a number and that any rational exponent m over n can be used to represent roots of numbers. The video also shows how to simplify expressions containing radical signs by using the rules of exponents and how to rewrite radical expressions using exponents.

This video explains that there are an infinite number of rational and irrational numbers and that the combination of these two groups is called real numbers. We review the concept of roots and radicals and show how to add and subtract real numbers as long as they have the same base and the same index. The video also demonstrates how to simplify complex expressions by factoring and using exponents. It concludes by discussing the concept of multiplication and division of real numbers.

This video discusses the concept of rationalizing the denominator when working with fractions involving irrational numbers. It explains how to multiply the top and bottom of the fraction by the denominator to obtain a rational number, and demonstrates this process through several examples. The video also introduces the concept of the rationalizing factor, which is the expression that is multiplied by an irrational expression to obtain a rational number. The video concludes by discussing identities for multiplying radical expressions and applying these identities to simplify expressions with radicals.

This video describes how to plot the square root of a decimal number on the number line using a combination of circles, chords, and right-angled triangles. It also brings back the concept of the rationalizing factor and demonstrates how to simplify fractions involving irrational numbers.

In this video, we will be exploring the concept of polynomials and how they are used in various aspects of our daily lives. A polynomial is an algebraic expression made up of terms that are connected using addition or subtraction. The terms themselves consist of a coefficient, which is a fixed number, and a variable, which is a combination of one or more lowercase letters raised to a whole number. We will also discuss the concept of monomials, binomials, and trinomials, which refer to polynomials with one, two, and three terms respectively. Throughout the video, we will provide examples to help illustrate these concepts and make them easier to understand.

In this video, we will be exploring the concept of polynomial equations and how to solve them using graphs. We will begin by revisiting the concept of a polynomial, which is an algebraic expression made up of terms that are connected using addition or subtraction. We will also discuss the different types of polynomial equations, including linear, quadratic, and cubic polynomials. Linear polynomials are represented by straight lines, quadratic polynomials are represented by "U" shaped curves, and cubic polynomials are represented by roller coaster-like curves with hills and valleys.

When the pigs turn the tables and launch themselves at the birds, crushing their nests under their bellies, the birds must use math to find the zeros of a quadratic polynomial and build a shelter to protect themselves. Can they outsmart the pesky pigs and win the challenge, or will their nests be destroyed? Tune in to find out and learn about the important concept of calculating zeros in a polynomial.

This video provides examples to demonstrate the process of adding, subtracting, and multiplying polynomials and shows how to simplify the resulting expressions. We also touch upon the concept of like terms and distributive property.

This video provides an example of using polynomial division to find the average expenditure per person on movie tickets in the United States from 1990 to 1995. The method described for dividing polynomials is similar to long division with whole numbers, except it involves constants and variables.

In this video, the concepts of remainder theorem and factor theorem are explained as a way to simplify the process of factoring polynomials. The remainder theorem states that if you divide a polynomial (f of x) by a linear polynomial (x minus h), then the remainder is given by (f of h). This means that the remainder can be found by evaluating the polynomial when x equals h, rather than carrying out the lengthy process of long division. The factor theorem states that if (x minus h) is a factor of a polynomial (f of x), then (f of h) is equal to zero. An example is provided to demonstrate how these theorems can be used to find the remainder and factors of a polynomial without using long division.

When a realm of Norse gods is captured by ice giants, the only way for the Asgardians to reclaim their world is by crossing a 130 meter long bridge made of light. Zoomus, a god with the ability to run at 23 meters per second, must find out if he can cross the bridge before it flickers off in less than 15 seconds. Using Newton’s second equation of motion, we will help Zoomus determine the roots of the quadratic equation to see if he has a chance at stopping the ice giants and returning to Asgard. Tune in to find out if Zoomus will succeed in his mission.

This video explains how to use the rational roots test to factorize cubics, polynomials with a highest exponent of 3. The rational roots test states that the solutions to a polynomial can be found by dividing a factor of the constant term by a factor of the leading coefficient. It’s also a refresher for students wanting to learn polynomial long division and factorisation of quadratic polynomials #polynomialfactorization #cubicequations #rationalrootstest

In this video, we will learn how to factor quadratic equations that are the "difference of squares", or expressions of the form "a-squared minus b-squared". By recognizing this form, we can use the factors (a plus b) and (a minus b) to solve for the zeros of the quadratic function. We will also see how to apply this method to different examples and how the zeros of these factors are the same as the zeros of the corresponding quadratic function. #quadraticequations #factoring #algebra

In this video, we will learn how to factor quadratic equations that are the "perfect squares", or expressions of the form "(a plus b) whole squared or (a minus b) whole squared.". By recognizing this form, we can rewrite them as "a-squared plus 2ab plus b-squared" and "a-squared minus 2ab plus b-squared". #quadraticequations #factoring #algebra

In the video, we introduce a new algebraic identity to calculate the product of two four-digit numbers, 1998 and 2004, by expressing them as the product of the binomials (2000 minus 2) and (2000 plus 4). The identities we have learned so far are all special cases of this all-weather identity, which allows for the calculation of the product of (x plus a) and (x plus b) and can be used to factorize more complex polynomials. #quadraticequations #factoring #algebra #binomials

In this video, the concept of multiplying trinomials (three terms) is introduced. The graphical approach involves dividing a square sheet of paper with dimensions equal to the sum of the three terms into nine smaller pieces, and determining the areas of these pieces. The sum of these areas is equal to the square of the trinomial. The concept is demonstrated using the example of (3x + 4y + 5z) squared, where 'a' is equal to 3x, 'b' is equal to 4y, and 'c' is equal to 5z. The resulting identity for the trinomial is then used to expand or factorize polynomials.

This video explains how to multiply polynomials, by breaking them down into smaller pieces and examining their individual volumes. The process involves making markings on the sides of the trinomial, such as a cube, and cutting them along those markings to create smaller pieces. The sum of the volumes or areas of the smaller pieces is equal to the cube of the original trinomial. The video gives an example of using this process to expand the expression (a + b)^3 and demonstrates how to use the resulting identity to factorize polynomials. The video also explains that this process can be extended to multiplying higher order polynomials by breaking them down into smaller pieces and examining their individual volumes or areas.

This video explains how to use the sum of cubes identity, which states that a-cubed plus b-cubed can be expressed as (a+b) times (a-squared - ab + b-squared), to factorize and expand polynomials. The identity is demonstrated through various examples, including ones with complex terms.

This video explains how to use the difference of cubes identity, which states that a-cubed minus b-cubed can be expressed as (a-b) times (a-squared + ab - b-squared), to factorize and expand polynomials. The identity is demonstrated through various examples, including ones with complex terms.

The video discusses how to evaluate cubic equations efficiently by using the identity that x-cubed plus y-cubed plus z-cubed plus 3xyz is equal to (x plus y plus z) times (x squared + y squared + z squared – x times y  – y times z – x times z)

Welcome to a journey through the world of Cartesian coordinates! Have you ever struggled to find your way around a new city or neighborhood? Well, in this video, we'll take you back to the 17th century to learn how French mathematician Rene Descartes stumbled upon the concept of the Cartesian coordinate plane. You'll learn how to use coordinates to identify points on a graph, and how to plot and distinguish between points using the x and y axes. We'll also explore how to use ordered pairs to make it easier to describe points on a graph. So join us and master the art of navigation in the world of math!

In the midst of an exciting adventure, demigod Apollo finds himself trapped in a deadly maze where man-eating giants plan to cook him for dinner. With the help of his phoenix, Apollo must navigate to six points within the maze to collect fragments of a magical stone in order to escape. To guide his phoenix, Apollo must find the cartesian coordinates of each point on the coordinate plane. But with no coordinates marked on his map, can Apollo outsmart the giants and escape the maze to freedom? Follow along to find out in this thrilling tale of math and bravery.

When the cunning Professor X begins committing robberies across the city, it's up to detective Sherlock Holmes to use math to track down the criminal and bring him to justice. Using the coordinates of previous crime scenes, Sherlock plots the points on a coordinate plane to reveal Professor X's pattern and predict his next move. Don't miss this thrilling adventure of problem-solving and math concepts as Sherlock uses the power of geometry to catch the notorious Professor X.

Join Rachel and Phoebe as they battle it out to beat their friend Monica's coffee sales record at the annual Coffee Craze fundraiser. But with two different types of coffee on offer, Cappuccino and Latte, the girls must use their math skills to set up a linear equation in two variables to figure out how many cups of each they need to sell. Follow their journey as they discover the infinite number of solutions to their equation, and use graphs to better understand the relationship between their sales. This educational and entertaining film is perfect for anyone looking to brush up on their linear equations and graphing skills.

When Dexter's beloved AI robot, C3PO, gets lost in a virtual maze, he must use his knowledge of horizontal and vertical lines to guide his robot to safety. Follow Dexter on his journey as he learns about the equations of lines parallel to the x and y axes of a coordinate plane. Will Dexter be able to rescue C3PO and complete his programming mission? Tune in to find out.

In the mystical land of Kung Fu, a math professor named Shifu sets out on a quest to find the coordinates of an ancient academy carved into a nearby mountain. With the help of the wise monk Oogway, Shifu uses the graph of linear equations in two variables to determine the correct location of the academy and save it from being lost forever. Follow Shifu on his journey as he uses math to solve the mystery and bring peace to the Valley of Peace.

Read on to learn the basics of Euclidean Geometry before we dive into more complex concepts.

Pythagoras and his group discovered many geometric properties and developed the theory of geometry to a great extent. This process continued till 300 BC. At that time Euclid, a teacher of mathematics at Alexandria in Egypt, collected all the known work and arranged it in his famous treatise, called ‘Elements’. He divided the ‘Elements’ into thirteen chapters, each called a book. These books influenced the whole world’s understanding of geometry for generations to come.

In this module, we shall discuss Euclid’s approach to geometry and shall try to link it with present-day geometry.

In this video, we will explore how architects employed by the Italian government used lines and angles to carefully calculate the amount of soil that needed to be removed from the ground to reduce the tilt of the leaning tower of Pisa to a safer angle of 4 degrees. We will also see how the miscalculation of angles by the flight control software of the Boeing 737MAX led to a tragic plane crash, costing the lives of 189 people. Through these examples, we will see the crucial role that lines and angles play in the stability and safety of structures and systems in our world. Tune in to learn more about the real-life applications of lines and angles.

In this video, we'll be using the game of snooker to illustrate geometric concepts like points, lines, rays, line segments, and different types of angles. Whether you're a student looking to brush up on your geometry or just curious about the math behind snooker, this video has something for everyone. So grab your cue and let's get started!

Join twin brothers Billy and Ronnie as they compete in the Pizza Bros International Championship in this exciting lesson on pairs of angles. Follow along as they use their knowledge of supplementary angles, complementary angles, adjacent angles, the linear pair postulate, and vertically opposite angles to devise a plan to win the championship and earn a lifetime supply of delicious pizza. Whether you're a fan of math or just love a good slice, this video is not to be missed.

When a young Greek mathematician named Eratosthenes sets out to estimate the Earth's circumference, he has no idea that his simple experiment will change the way we understand math forever. Eratosthenes laid the foundations of the various angles that are formed when a transversal intersects two straight lines including alternate interior angles, alternate exterior angles, corresponding angles, co-interior angles, and co-exterior angles. We'll also cover the important concept of parallel lines and how angles mentioned above become equal to each other when the two lines cut by the transversal are parallel. This is a crucial concept in geometry, and understanding it will help you solve a wide range of problems.

On the island nation of Freedonia, President Petra Immova is under pressure to resign due to the blocking of the Freedonian Canal by the world's largest ocean tanker, Seagallop. In order to remove Seagallop, President Immova must measure the angles of the wedges that will be used to push the tanker from both sides of the canal. However, the second angle can only be measured by accessing the neighboring nation of Carovia, which Immova refuses to do. Can Immova find a way to calculate the second angle without negotiating with the hostile Carovian King? Tune in to find out as we explore the alternate interior angles theorem.

In this action-packed episode, scientists Didi and Dexter are on a mission to save the world from a deadly virus that has contaminated their lab. As they navigate their way through the parallelogram-shaped command centre, they must use their knowledge of the alternate exterior angle theorem to dispense the antivirus in the contaminated rooms without exposing themselves to the virus. Will they be able to save the day and defeat the virus? Tune in to find out!

Sheldon is a child prodigy who has been working in Professor Zeebo's physics laboratory. When the professor accidentally falls through an interdimensional portal, Sheldon must use all of his knowledge to try and bring him back. With the help of a protractor, Sheldon will try to prove that two lines are parallel to each other by showing that a pair of alternate interior angles are equal. Will Sheldon be able to rescue the professor and bring him back home safely? Tune in to find out.