This article suggests the introduction of the concepts of areas bounded by plane curves and the volumes of solids of revolution in Pre-calculus. It builds on the basic knowledge that students bring to a pre-calculus class, derives a few more formulas, and gives examples of some problems on plane areas and the volumes of solids of revolution that…

PreCalculus students can use the Completing the Square Method to solve quadratic equations without the need to memorize the quadratic formula since this method naturally leads them to that formula. Calculus students, when studying integration, use various standard methods to compute integrals depending on the type of function to be integrated.…

In terms of modern pedagogy, having visual interpretation of trigonometric functions is useful and quite helpful. This paper presents, pictorially, an easy approach to prove all single angle trigonometric identities on the axes. It also discusses the application of axial representation in calculus--finding the derivative of trigonometric functions.

Interesting problems sometimes have surprising sources. In this paper we take an innocent looking problem from a calculus book and rediscover the radical axis of classical geometry. For intersecting circles the radical axis is the line through the two points of intersection. For nonintersecting, nonconcentric circles, the radical axis still…

In a well-known calculus problem, an open top box is to be made from a rectangular piece of material by cutting equal squares from each corner and turning up the sides. The task is to find the dimensions of the box of maximum volume. Typically, the length of the sides of the corners that produces the largest volume turns out to be an irrational…

Twelve unusual problems involving divisibility of the binomial coefficients are represented in this article. The problems are listed in "The Problems" section. All twelve problems have short solutions which are listed in "The Solutions" section. These problems could be assigned to students in any course in which the binomial theorem and Pascal's…

In their sections on inverses most precalculus texts emphasize an algorithm for finding f [superscript -1] given f. However, inspection of precalculus and calculus texts shows that students will never again use the algorithm, which suggests the textbook emphasis may be misplaced. Inverses appear primarily when equations need to be solved, which…

How did it happen that both full-time and adjunct faculty at Scottsdale Community College embrace a standards-based curriculum from beginning algebra through differential equations? Simply put, it didn't just happen. Not only did it take well over a decade, but it was also the result of a sequence of initiatives, decisions, discussions, targeted…

The cross-product is a mathematical operation that is performed between two 3-dimensional vectors. The result is a vector that is orthogonal or perpendicular to both of them. Learning about this for the first time while taking Calculus-III, the class was taught that if AxB = AxC, it does not necessarily follow that B = C. This seemed baffling. The…