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The Introductory Algebra DVD series consists of 31 segments each on its own DVD, totaling approximately 12 hours of video instruction. Topics include fractions, real numbers, exponents, solving linear equations and inequalities and application, polynomials, factoring, rational expressions, ratio and proportions, graphing linear equations and inequalities and equations of lines, functions, systems of linear equation and inequalities, radicals, rational exponents, solving quadratic equations. Many of the topic titles are the same as for the intermediate algebra series, but at a level consistent with beginning algebra courses.
Segments included in this series:
This segment covers simplest form as well as addition, subtraction, multiplication and division of fractions.
- Operations on Real Numbers.
This segment covers Addition, subtraction, multiplication, and division of signed numbers. Absolute value and opposites are also included.
- Exponents, order of Operations, and Introduction to Variables.
This segment covers an introduction of exponents by raising signed numbers (including fractions) to positive integral powers. Order of operations is also covered as well as an introduction to variables. Evaluating an expression by substituting given replacement values for variables is included.
This segment covers the definition of a term, like terms, and numerical coefficients. The distributive property is used to combine like terms.
- Solving Linear Equations.
This segment covers the solution of linear equations, balancing equations, isolation of the unknown, and moving terms from one side of the equation to the other. Removal of parentheses and simplification of terms is covered as well as collecting like terms.
- Applications of Linear Equations.
This segment covers steps that may be used to solve applications. Translating phrases into expressions is included as well as solving applications by setting up and solving linear equations.
- Solving Linear Inequalities.
This segment covers solving linear inequalities by isolating the unknown using methods similar to those for linear equations. The reversal of the inequality symbol when multiplying both sides of an inequality by a negative number is also covered.
This segment covers the laws of exponents and their use in simplifying algebraic expressions. This segment includes negative exponents.
- Operations on Polynomials.
This segment covers addition, subtraction, multiplication, and long division of polynomials. The First, Outer, Inner, Last (FOIL) method for multiplying a pair of binomials is also covered.
This segment covers factoring of polynomials beginning with factoring out the greatest common factor. In the case of trinomials the method of arranging terms in descending degree and inspection of signs to locate signs in the factors is covered. In the case of polynomials with four or more terms, the method of factoring by grouping is covered.
This segment covers factoring binomials in the case of the difference of two perfect squares and in the case of the sum or difference of two cubes. The case of binomials which reduce to these cases after factorization of the greatest common factor is also covered.
- Solving Quadratic Equations by Factoring.
This segment covers the method of solving quadratic equations by first rearranging terms so as to force one side of the equation to be identically zero and then factoring the resulting trinomial or binomial. The factors are then used to obtain linear equations for the solutions.
- Rational Expressions - I.
This segment covers multiplication and division of rational expressions as well as reducing to lowest terms by factoring both numerator and denominator. In case of multiplication the use of dividing out common factors before multiplication to simplify work is covered.
- Rational Expressions - II.
This segment covers addition and subtraction of rational expressions by finding the least common denominator after factoring all denominators. This segment also covers simplifying complex fractions.
- Equations with Rational Expressions.
This segment covers methods for solving equations involving rational expressions which can be reduced to either linear or quadratic equations on multiplication of both sides of the equation by the least common denominator of all denominators in the equation. The notion of elimination of extraneous roots or solutions by checking all solutions in the original equation is also covered.
This segment covers a definition of ratio as well as three ways of writing ratios. Proportions are solved by setting cross products equal, and applications are solved by setting up and solving proportions.
- Applications with Rational Expressions.
This segment covers solving applications by setting up and solving equations that contain rational expressions.
- Graphing Linear Equations.
This segment covers graphing lines in the plane using rectangular coordinates via the method of tabulating and plotting points which satisfy the equation of the line.
- Slope and Equations of Lines.
This segment covers the slope formula and finding the slope of a line by using the slope-intercept form of a line. Horizontal and vertical lines are included.
- Slope and Graphing Inequalities.
This segment covers the slope-intercept and point-slope forms for the equation of a line. The relationship of slope to steepness and methods of calculating slope via rise over run as well as rearrangement into slope-intercept form is covered. Parallel and perpendicular lines are also covered as well as graphing inequalities by graphing their boundary equations and using a test point off the boundary to determine the solution region.
This segment covers the solution of systems of pairs of linear equations by both the method of elimination (sometimes called the method of addition or the method of row reduction for large systems) and the method of substitution. Graphical representations and notations of dependence and of inconsistency of parallel pairs are also covered.
This segment covers applications of two equations in two unknowns.
- Introduction to Radicals.
This segment covers principal square root and nth roots in general. Simplifying radical expressions is covered including radicals containing variables.
- Adding and Subtracting Radicals.
This segment covers like radical expressions as well as adding and subtracting radical expressions.
- Multiplying and Dividing Radicals.
This segment covers multiplying radical expressions and rationalizing denominators.
- Radical Equations and Applications.
This segment covers solving equations containing square roots. A distance formula application is included.
- Systems of Linear Inequalities.
This segment covers solving systems of linear inequalities in two variables by graphics.
This segment covers the definition of a rational exponent. Also, expressions containing rational exponents are simplified using laws of exponents. The problems covered here are at the beginning algebra level of difficulty.
- Solving Quadratic Equations by Completing the Square.
This segment covers solving quadratic equations by the square root method, as well as solving quadratic equations by completing the square. The problems covered here are at the beginning algebra level of difficulty.
- Solving Quadratic Equations by the Quadratic Formula.
This segment covers the quadratic formula and its use in solving quadratic equations. This segment also covers writing a quadratic equation in standard form in order to identify appropriate coefficient in the quadratic formula.
- Complex Solutions of Quadratic Equations and Graphing Quadratic Equations.
This segment covers an introduction to complex numbers, operations on complex numbers, and complex solutions of quadratic equations. This segment also covers graphing quadratic equations in two variables by including methods for finding the vertex and x and y intercepts.
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