Video Segment 1: Introduction
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This video presents several mathematical themes and emphasizes why algebra is important in practical life.
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Video Segment 2: The Language of Algebra
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This video provides a survey of basic mathematical terminology. Content includes properties of the real number system and the basic axioms and theorems of algebra. Specific terms covered include algebraic expression, variable, product, sum term, factors,
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Video Segment 3: Exponents and Radicals
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This video explains the properties of exponents and radicals: their definitions, their rules, and their applications to positive numbers. As an example on how to use the Rules of Exponents, a discussion of the O-ring failure of the Challenger Space Shuttle.
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Video Segment 4: Factoring Polynomials
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This video defines polynomials and describes how the distributive property is used to multiply common monomial factors with the FOIL method. It covers factoring, the difference of two squares, trinomials as products of two binomials, among other subjects.
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Video Segment 5: Linear Equations
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This video introduces equations. It shows how solutions are obtained, what they mean, and how to check them using one unknown. An example of how linear equations are used in real life involving a sewage plant near Los Angeles.
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Video Segment 6: Complex Numbers
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This video adds complex numbers Ñ their definition and their use in basic operations and quadratic equations. Explanations are given on how to combine like terms, apply the FOIL method, and rationalize the denominator for finding the product or quotient.
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Video Segment 7: Quadratic Equations
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This video reviews the quadratic equation and covers standard form, factoring, checking the solution, the Zero Product Property, and the difference of two squares.
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Video Segment 8: Inequalities
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This video shows the properties and solution of inequalities, linking positive and negative numbers to the direction of the inequality.
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Video Segment 9: Absolute Value
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In this video, the concept of absolute value is defined, enabling the use of it in equations and inequalities. There are two examples to show for this.
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Video Segment 10: Linear Relations
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This video looks at the linear relationship between two variables, expressed as a set of ordered pairs.
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Video Segment 11: Circle and Parabola
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In this video, the circle and parabola are presented as two of the four conic sections explored in this series
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Video Segment 12: Ellipse and Hyperbola
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In this video, the ellipse and hyperbola, the other two conic sections examined in the series, are introduced. The video defines the two terms, distinguishing between them with different language, equations, and graphic representations.
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Video Segment 13: Functions
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This video defines a function, discusses domain and range, and develops an equation from real situations. As a demonstration of functions, pizza and encoding secret messages provide excellent examples.
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Video Segment 14: Composition and Inverse Functions
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In this video, graphics are used to introduce composites and inverses of functions as applied to calculation of the Gross National Product. One-to-one functions and the horizontal line test are introduced.
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Video Segment 15: Variation
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In this video, examples are given of special functions in the form of direct variation and inverse variation, with a discussion of combined variation and the constant of proportionality. These are explored in relation to polynomials and assorted equations.
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Video Segment 16: Polynomial Functions
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This video explains how to identify, graph, and determine all intercepts of a polynomial function. It covers the Polynomial Functions; real numbers; exponents; and linear, quadratic, and cubic functions.
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Video Segment 17: Rational Functions
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This video explains that a rational function is the quotient of two polynomial functions. The properties of these functions are investigated using cases in which each rational function is expressed in its simplified form.
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Video Segment 18: Exponential Functions
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This video teaches the exponential function, as illustrated through formulas. The population of Massachusetts and radioactive decay are just a few of the examples that are used throughout this video.
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Video Segment 19: Logarithmic Functions
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This video covers the logarithmic relationship, the use of logarithmic properties, and the handling of a scientific calculator. How radioactive dating and the Richter scale depend on the properties of logarithms is explained.
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Video Segment 20: Systems of Equations
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The case of two linear equations in two unknowns is considered throughout this video. Elimination and substitution methods are used to find single solutions to systems of linear and nonlinear equations.
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Video Segment 21: Systems of Linear Inequalities
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In this video, elimination and substitution are used again to solve systems of linear inequalities. This technique can be seen through problems in the Berlin airlift, the production of butter and ice cream, and other situations are given.
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Video Segment 22: Arithmetic Sequences and Series
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This video differentiates between arithmetic and non arithmetic sequences as it presents the solutions to sequence- and series-related problems. Definitions include sequence, arithmetic sequence, arithmetic series, fixed number, and common difference.
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Video Segment 23: Geometric Sequences and Series
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This video provides examples of geometric sequences and series (f-stops on a camera and the bouncing of a ball), explaining the meaning of nonzero constant real number and common ratio.
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Video Segment 24: Mathematical Induction
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In this video, mathematical proofs applied to hypothetical statements shape this discussion on mathematical induction. This segment exhibits special cases, looks at the development of number patterns, relates the patterns to PASCAL's triangle and factorial
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Video Segment 25: Permutations and Combinations
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This video shows techniques for counting the number of ways in which collections of objects can be arranged, ordered, and combined are demonstrated. Answers to questions such as, "how many variations of a license plate number or poker hand are possible?"
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