A strong Algebra background is a prerequisite for further study in mathematics and science, and for students studying a wide variety of college majors, College Algebra is part of their graduation requirements. Professors teaching College Algebra assume that their students have mastered Pre-Algebra, Elementary Algebra (Algebra 1), and Intermediate Algebra (Algebra 2).
The time constraints that exist in a traditional lecture based course, make it impossible for an instructor to slow down enough to explain in detail much of the prerequisite information that is required to follow the examples in a College Algebra course. As a result, many students find themselves lost in class. They simply need more examples, more time with those examples, and a more detailed set of explanations with those examples. That is where College Algebra videos can help.
There are hundreds of traditional Algebra textbooks in print today, but it is hard for many students to read a dry Algebra textbook. Quality Algebra tutoring would be the best solution for students who need additional help, but quality Algebra tutoring is often very expensive, hard to find, and inconvenient. A comprehensive set of College Algebra videos is an affordable alternative.
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0. Prerequisite Topics
This chapter covers, in detail, many of the prerequisite topics which must be mastered before starting College Algebra.
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1. Equations & Inequalities
This chapter covers the techniques required to find solutions for various types of equations. The topics include: linear equations, quadratic equations, complex numbers, radical equations, higher order polynomial equations, and inequalities.
2. Graphs in the Cartesian Plane
This chapter covers the techniques required to graph equations in the rectangular coordinate system. The topics include: distance, slope, midpoint, intercepts, symmetry, lines, and circles.
This chapter covers the properties of functions, a library of functions, and graphs of functions. The topics include: relations, the definition of a function, domain, range, the difference quotient, graphing functions, average rate of change, maxima, and transformations.
4. Linear & Quadratic Functions
This chapter further explores the properties of functions, their graphs, and their applications. The topics include: linear functions, demand, revenue, quadratic functions, vertices, axes of symmetry, intercepts, domain, range, extrema, and applications of functions.
5. Polynomial & Rational Functions
This chapter covers polynomials and rational functions. The topics include: polynomial functions, the degree of a polynomial, graphing polynomials, zeros, multiplicity, turning points, end behavior of graphs, domain, range, vertical asymptotes, horizontal asymptotes, slant (or oblique) asymptotes, graphing rational functions, rational and polynomial inequalities.
6. Exponential & Log Functions
This chapter covers exponential and log functions. The topics include: function composition, domain of a composite function, inverse functions, one-to-one functions, graphs of inverse functions, finding inverse functions, graphing exponential functions, solving exponential equations, writing exponential equations into log form, graphing logarithmic functions, solving logarithmic equations, writing log equations into exponential form, properties of logs, and equations of quadratic form.
7. Systems of Equations
This chapter covers some techniques to solve systems of equations. The topics include: solving systems of linear equations by substitution, solving systems of linear equations by elimination, and solving nonlinear systems by substitution and elimination.