Advantages of representing ternary and quaternary composition diagrams by means of rectangular coordinates were pointed out in a previous paper (EJ 288 693). A further advantage of that approach is that analytic geometry, based on rectangular coordinates, is directly applicable as demonstrated by the examples presented. (JN)

A sequential but non-axiomatic high school geometry course which includes Euclidean, transformation, and analytic geometry and vectors and matrices, and emphasizes the invariance property of transformations, is outlined. Sample problems, solutions, and comments are included. (MN)

This article begins with a comparison of two groups of teachers, working on the same tasks in Analytic Geometry. One group has only basic experience in CAS-assisted problem solving, and the other group has extensive experience. The comparison is discussed in terms of the interplay between reflection, operative knowledge and execution. The findings…

The purpose of this revised syllabus/guide is to help teachers and administrators plan and implement Course II in the the State Three-Year Sequence for High School Mathematics for Regents credit. Course II builds upon the state mathematics curriculum outlined in the department's mathematics K-6, Grade 7, Grade 8, and Course I publications.…

The goals, objects, materials and grade levels are specified in this description of a laboratory activity involving analytic geometry concepts. Students mark out bicycle gymkhana courses in which directions to participants are given by Cartesian coordinates. (JP)

Illustrates various methods to determine the perimeter and area of triangles and polygons formed on the geoboard. Methods utilize algebraic techniques, trigonometry, geometric theorems, and analytic geometry to solve problems and connect a variety of mathematical concepts. (MDH)

The curriculum recommendations of the Advisory Commission on Articulation Between Secondary Schools and Ohio Colleges are presented, along with the recommendations of the Advisory Council for College Preparatory Education. The recommendations for college preparatory science programs include the laboratory experiences and scientific vocabulary, as…

A GUIDE FOR A 1-YEAR COURSE IN DIFFERENTIAL AND INTEGRAL CALCULUS PREREQUISITED KNOWLEDGE IN ALGEBRA, ANALYTIC TRIGONOMETRY, AND ELEMENTARY ANALYSIS. EACH ASSIGNMENT CONTAINED BOTH NEW AND REVIEW WORK TO REINFORCE THE NEW WORK. THERE WERE ELEVEN UNITS OF STUDY USING THE FOLLOWING FOUR BOOKS--"CALCULUS AND ANALYTIC GEOMETRY, THIRD…

Based on a sequence of number pairs, a recent paper (Mauch, E. and Shi, Y., 2005, Using a sequence of number pairs as an example in teaching mathematics, "Mathematics and Computer Education," 39(3), 198-205) presented some interesting examples that can be used in teaching high school and college mathematics classes such as algebra, geometry,…

Explains the use of the 3-dimensional analytic geometry method to find values for a field geology problem. Gives a description of the mathematical theory for this method which can be applied to data obtained by drilling as well as open surfaces, and a computer program. (RT)

Presents examples of using a tic-tac-toe format to practice finding the slope and identifying parallel and perpendicular lines from various equation formats. Reports the successful use of this format as a review in both precalculus and calculus classes before students work with applications of analytic geometry. (JRH)

Evidence on the decline in preparation of entering calculus students and the relationship to high school preparation is presented, focusing on the trend toward the de-emphasis of trigonometry and analytic geometry in favor of calculus. Data on students' perception of the adequacy of their preparation are also presented. (Author/MN)

Sixteen beginning analytic geometry and calculus classes (442 students) followed eight testing regimes for one academic quarter. Three aptitude subgroups were identified in each class. Classes to which daily quizzes were given achieved significantly higher on a specially constructed test than those which had only a single midterm examination.…

Provides examples in which graphs are used in the statements of problems or in their solutions as a means of testing understanding of mathematical concepts. Examples (appropriate for a beginning course in calculus and analytic geometry) include slopes of lines and curves, quadratic formula, properties of the definite integral, and others. (JN)

This document is a guide to the advanced placement program in calculus for grade 12 in the city schools in Warren, Ohio. The program covers analytic geometry, differential and integral calculus of algebraic functions, elementary transcendental functions, and applications of differentiation and integration. The philosophy and aims of the program…