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Algebraic Expressions are mathematical expressions that use letters as well as numbers to represent more general situations. This chapter will introduce inequalities, equations and how to solve then using mathematical rules.
An inequality compares the relative size of two values. In this lesson we will review the basic inequality symbols and basic operations on inequalities.
In this lesson we will use the basic operations on inequalities to solve for an unknown quantity in a simple inequality.
In this important chapter, we will learn the basic operations that can be applied to an equation. Specifically, we will learn how to solve a simple equation.
This chapter will introduce the basics of exponents.
This chapter will introduce the basics of exponents.
In this chapter, the Virtual Teacher will work with the student to gain a solid understanding of scientific notations. Using interactive animations, the student will build a practical understanding of this concept.
In this chapter, we will go through the basic laws of exponents.
In this topic, the Virtual Teacher will introduce the student to polynomials and some of the common operations that can be applied to them.
Linear Relations are the most basic relations. In this chapter, we will learn how to build tables of values for linear functions, and how to derive a linear function given two values.
In this introduction to linear relations we will see how real-life problems can be expressed as linear relations.
The rate of change measures how 'fast' a relation changes given a change in the 'x' (independent) variable. In this chapter, we will learn how to compute it.
In this lesson we will learn to derive a linear relation algebraically, using the standard form y = a x + b.
The Pythagorean Theorem is a foundational theorem for much of basic geometry. We will learn its basics, how to apply it, and the basics of distance calculation in the Cartesian plane.
In this lesson we will be introduced to the Pythagorean theorem using the areas of the squares. This gives a better visual understanding of this important theorem.
This chapter contains a single application of the Pythagorean Theorem for now. As schools and teachers request more examples, our educators can generate more complex cases.
In this lesson, we will be introduced to the Cartesian Plane. Specifically, how to use the Pythagorean Theorem to compute distances in such a plane.
In this topic, we will look at the basics of functions. The dynamic and interactive lessons will give the student a very good understanding of what functions are, their properties, and the basic transformations that we can apply to them.
In this chapter, the Virtual Teacher will start with the concept of relations. A number of hands-on interactive lessons will ensure the student gets a solid understanding of relations before moving on to functions.
Building upon a good understanding of relations from previous lessons, the Virtual Teacher will now go through interactive animations to explain what functions really are.
Now that the concepts of Relations and Functions are defined, these lessons will go through the basic properties of functions. These definitions are very important as they will come up quite often when working with functions in future lessons.
In this chapter, we will consider the basic transformations that we can apply to functions in the Cartesian plane.
In this major topic, the Virtual Teacher will take the student through advanced concepts in functions, including function composites, absolute function, square root and step functions.
This dynamic chapter explains the basics of function notation. This knowledge is essential for future lessons so the student is able to read the shown function descriptions.
In this chapter, the Virtual Teacher will explain dynamically what is the inverse of a function. Through a number of practical examples, the student should get a good understanding of how to work through the process on his / her own.
In what is probably a simpler concept than it first appears, the Virtual Teacher will go through the theory and a number of interactive examples where the student will work on evaluating the inverse of a given function.
This chapter deals with the inverse function as a starting point for rational functions. The peculiarities of the inverse function are viewed in detail to give the student a sound understanding.
Quadratic Functions are essential in modern Algebra. In this topic, we will get a solid understanding of quadratic functions and how to solve them.
In this series of dynamic lessons, quadratic functions are studied in great detail.
The standard form is useful when plotting or trying to solve quadratic functions. In this topic, we will get introduced to the standard form and learn how to convert back and forth from the general form.
In this chapter, we will learn how to solve quadratic equations. The Virtual Teacher will guide the student through the common methods.
This simple chapter formally introduces the concept of absolute value function.
In this chapter, the basics of the absolute function will be introduced.
Building upon the basics of the absolute value function, the student will learn how to transform this function. The Virtual Teacher will go back to basics when so that the concepts learned can be applied to any function transformation.
In this dynamic chapter, the Virtual Teacher will go through some practical examples to explain how to solve inequalities involving absolute functions.
In this chapter, square root function will be considered.
The square root function is a basic notion in algebra. In this chapter, the Virtual Teacher will go through some of the basics of the square root function.
Building upon the concepts learned in previous chapter, along with the acquired knowledge about function transformations, this chapter deals with the impact of transformations on the square root function.
Step functions are interesting mathematical tools. They are often viewed as 'non-traditional' as they involve an 'algorithmic' side. This chapter will make it easy for the student to deal with step functions using practical examples.
The Exponential and Logarithmic functions are very important in many scientific disciplines. In this topic, the Virtual Teacher will go through the basics using interactive and dynamic examples.
This chapter introduces the exponential function, its base and its basic properties.
This chapter will explain succintly the basics of solving equations with exponential functions.
In this interactive chapter, the Virtual Teacher will work with the student to represent real-life problems with an exponential function.
The Logarithmic function is the inverse of the exponential function with the same base. This chapter introduces the logarithmic function and its properties. The concepts are reinforced with many dynamic examples.
Building upon what we have learned so far, this interesting chapter explains the basic laws of logarithms. These laws are often critical for solving exponential or logarithmic equations.
This interactive chapter goes through some interesting and interactive examples to apply many of the concepts learned earlier.
In this topic, the Virtual Teacher will explain the concept of factoring, and will illustrate with many examples.
In this Chapter, the Virtual Teacher will explain the basic factoring methods.
In this chapter, we will work with rational expressions, and learn how to simplify them.
In this chapter, we will go through the process of multiplying and dividing rational expressions.
In this chapter, a series of dynamic animations will teach the student the basics of adding and subtracting rational expression. Of particular important is the identifying and obtained the Lowest Common Divisor (LCD).
Quite often in engineering and sciences, we are faced with problems involving many variables. If we can construct a system of equations, we are often able to solve for the unknowns we are facing. This topic will go through the basics of solving simple systems of equations.
This chapter will cover the basics of systems of equations.
This chapter will take the student through the process of using the most common algebraic methods to solve simple systems of equations.
A semi-linear system of equation is one where one of the equations is non-linear. This chapter will show how to apply the algebraic methods to solving semi-linear systems of equations.
Conics is often viewed as a challenging concept for students. In this topic, the use of dynamic animations will help the student gain a solid understanding of this topic.
This graphical introduction will help the student visualize conic sections and surfaces. Such a comprehension is critical to be able to grasp more advanced notions in future lessons.
Starting with the most basic conic, the Virtual Teacher will explain the basic properties of circles and how to use the standard form to express or draw a circle graphically.
This chapter will cover in detail hyperbolas, starting from the definition to expressing their shape via the standard equation.
Parabolas were already viewed in some detail as the square function. This chapter will consider parabolas as conics and explain the standard function. Interactive examples will ensure student comprehension of this subject.
Parabolas were already viewed in some detail as the square function. This chapter will consider parabolas as conics and explain the standard function. Interactive examples will ensure student comprehension of this subject.
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