In this paper, the authors examine a property that holds for all cubic polynomials given two zeros. This property is discovered after reviewing a variety of ways to determine the equation of a cubic polynomial given specific conditions through algebra and calculus. At the end of the article, they will connect the property to a very famous method…

The mathematical topic of inverse functions is an important element of algebra courses at the high school and college levels. The inverse function concept is best understood by students when it is presented in a familiar, real-world context. In this article, the authors discuss some misconceptions about inverse functions and suggest some…

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. Nonroutine tasks encourage students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions. This…

This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos--satisfying an axiom sin[superscript 2] + cos[superscript 2] = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two…

A central goal of secondary mathematics is for students to learn to use powerful algebraic strategies appropriately. Research has demonstrated student difficulties in the transition to using such strategies. We examined strategies used by several thousand 8th-, 9th-, and 10th-grade students in five different school systems over three consecutive…

This article is in two parts: discussion of mathematical concepts involved in converting the reading from the tape-recorder counter which counts the turns of the run-off spool to that from the counter which counts turns of the take-up spool; calculating the length of tape run off when given the reading from the tape-recorder counter of the run-off…

The history of alligation problems as a part of the mathematics curriculum is briefly reviewed, and the non-unique nature of the solutions to many problems is discussed. (SD)

Examples of the presentation and solution of variations on a common projectile trajectory problem are presented. (BB)

Presented are eight student worksheets of block problems. Included are diagrams of the squares and hollow squares involved and a separate answer sheet for the problems. (CW)

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic, and contains problems related to diverse vocations. Solutions are provided for all problems. Problems presented in this package concern ratios used in food…

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume require solution of linear equations, systems…

This yearbook is a reference source of direct applications of mathematics for use in grades 7-12. Topics are listed alphabetically in each of four sections: arithmetic, algebra, geometry, and trigonometry. An explanation is given as to the plan of the book, making the location of desired material easier, and an index is included. In many cases the…

THis is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This volume includes problems involving logarithms, exponents, and…

Determines which chessboards contain a chromatic rectangle having all four corners the same color for any black-white coloring. Expands the problem to a three color problem. (YP)

Presented is the problem of determining alternative schedules for major league baseball. Equations of the schedule, conditions on the solutions, and solutions are discussed. (CW)