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Algebra : In Simplest Terms
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Mathematics — Study and Teaching
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1.

## Geometric Sequences and Series [electronic resource]

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. Finite and infinite geometric series and the sequence of partial sums are also defined in the discussion.
Online
1991
2.

## Functions [electronic resource]

Defines a function, develops an equation from real situations and discusses domain and range. The cutting of pizza and encoding of secret messages provide subjects for the demonstration of functions and their usefulness.
Online
1991
3.

## Exponents and Radicals [electronic resource]

Explains the properties of exponents and radicals: their definitions, their rules, and their applications to positive numbers. Shows how to use the Rules for Exponents to simplify expressions, demonstrating concepts through a discussion of the O-ring failure of the Challenger Space Shuttle.
Online
1991
4.

## Factoring Polynomials [electronic resource]

Defines polynomials and describes how the distributive property is used to multiply common monomial factors with the FOIL method. Covers factoring, the difference of two squares, trinomials as products of two binomials, the sum and difference of two cubes, and regrouping of terms.
Online
1991
5.

## Exponential Functions [electronic resource]

Covers graphing and developing the equation for an exponential function. Applications include bacteria growth, population growth, and radioactive decay.
Online
1991
6.

## Ellipse and Hyperbola [electronic resource]

Defines the two terms, distinguishing between them with different language, equations, and graphic representations. Architecture and surgery provide interesting application examples.
Online
1991
7.

## Composition and Inverse Functions [electronic resource]

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, and more encoded messages and the hazards of the bends in scuba diving provide instructive applications of the functions discussed.
Online
1991
8.

## Complex Numbers [electronic resource]

Focuses on complex numbers and their use in basic operations and quadratic equations. Students learn how to combine like terms, apply the FOIL method, and rationalize the denominator for finding the product or quotient of two complex numbers.
Online
1991
9.

## Circle and Parabola [electronic resource]

Using conic sections, provides a detailed look at circles and parabolas. Terminology and formulas for equations are discussed for each. The circle, its various measures when graphed on the coordinate plane (distance, radius, etc.), its related equations (e.g., center-radius form), and its relationships with other shapes are covered, as is the parabola with its various measures and characteristics (focus, directrix, vertex, etc.). An earthquake epicenter provides a real-life illustration.
Online
1991
10.

## Arithmetic Sequence and Series [electronic resource]

Differentiates between arithmetic and nonarithmetic sequences as it presents the solutions to sequence and series-related problems. Definitions include sequence, arithmetic sequence, arithmetic series, fixed number, and common difference.
Online
1991
11.

## Quadratic Equations [electronic resource]

Reviews the quadratic equation covering standard form, factoring, checking the solution, the Zero Product Property, and the difference of two squares. Environmental and aviation examples provide realistic problems that require the method of Completing the Square to solve them.
Online
1991
12.

## Rational Functions [electronic resource]

Defines a rational function as the quotient of two polynomial functions. Investigates the properties of these functions when each rational function is expressed in its simplified form. Clarifies the relationship between numerator and denominator using sign and other graphs to determine intercepts, symmetry, and asymptotes.
Online
1991
13.

## Mathematical Induction [electronic resource]

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 factorials, and elaborates the general form of the theorem.
Online
1991
14.

## Permutations and Combinations [electronic resource]

Demonstrates techniques for counting the number of ways that collections of objects can be arranged, ordered and combined. Uses examples from a poker hand and variations in license plate numbers.
Online
1991
15.

## Linear Relations [electronic resource]

Looks at the linear relationship between two variables, expressed as a set of ordered pairs. Students are shown the use of linear equations to develop and provide information about two quantities, as well as the applications of these equations to the slope of a line.
Online
1991
16.

## Linear Equations [electronic resource]

Covers how solutions for equations are obtained, what they mean, and how to check them using one unknown. Concepts are worked out in an application problem involving a modern sewage plant near Los Angeles, where a linear equation is set up and solved to determine how long to keep open an inlet pipe.
Online
1991
17.

## The Language of Algebra [electronic resource]

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, common factors, like terms, simplify, equation, sets of numbers, and axioms.
Online
1991
18.

## Introduction [electronic resource]

Introduces several mathematical themes and emphasizes why algebra is important in today's world.
Online
1991
19.

## Polynomial Functions [electronic resource]

Covers how to recognize, graph, and determine all of the intercepts of a polynomial function. Covers the role of coefficients; real numbers; exponents; and linear, quadratic, and cubic functions. Touches upon factors, x-intercepts, and zero values. These terms are demonstrated with the baking of pizza.
Online
1991
20.

## Variation [electronic resource]

Provides examples of special functions in the form of direct variation and inverse variation, with a discussion of combined variation and the constant of proportionality. These concepts are explored in relation to polynomials and assorted equations, with applications from chemistry, physics, astronomy, and the food industry.
Online
1991