Mathematics Projects  Pre-Calculus

Projects available:

Polynoimials and Trigonometry. TeX version or Postscript version

Project contributed by Neal Brand.
This project uses trigonometric identities to derive polynomials to approximate the sine and cosine functions. A fairly realistic story motivates the project.
Project teaches and provides practice in
• Approximation techniques
• Trigonometric identities
• Understanding differences between polynomials and transcendental functions.
• Use of symbolic mathematical software

Polynomials and the Exponential Function. TeX version or Postscript version.

Project contributed by Neal Brand.
This project uses the definition of the exponential function to derive a formula for a polynomial approximation to the exponential function. It assumes that students have seen the binomial theorem and have a good grasp of basic properties of polynomials.
Project teaches and provides practice in
• Algebraic manipulation
• Approximation techniques
• Understanding difference between polynomials and transcendental functions
• Use of symbolic mathematical software
• Asympototes for rational functions

Henry and the Fan. TeX version or Postscript version. If you use the TeX version then you should also download the figures in either postscript or CorelDraw format.

Project contributed by Neal Brand.
This project uses basic algebraic manipulation to maximize a class of functions. The story in the project is essentially true.
Project teaches and provides practice in
• Algebraic manipulation
• An introduction to Kirchhoff's law
• An introduction to maximizing functions
• Using graphing calculator or computer to make a conjecture
• Proving a conjecture

Life on Long Street. TeX version or Postscript version.

Project contributed by Neal Brand.
This project is an exercise in composition of functions. It could be assigned early in the semester or used in a college algebra course.
Project teaches and provides practice in
• Composition of functions
• Conjecturing and proving the conjecture

Trigonometric-Like Functions. TeX version or Postscript version.

Project contributed by Neal Brand.
This project is an introduction to the hyperbolic functions. It requires students to derive some basic identities involving hyperbolic functions which correspond to trigonometric identities they learned in class.
Project teaches and provides practice in
• Basic properties of the exponential function
• Algebraic manipulation
• Use of symbolic mathematical software

Lori and Jerry's Trail Optimization Problem. TeX version or Postscript version.

Project contributed by Neal Brand.
This projects introduces students to optimization problems similar to what they will see in calculus.
Project teaches and provides practice in
• Using graphs to guess maxima
• Proving a statement based on experimental data
• Some basic trigonometry
• Polynomial manipulation

A piece of Pi. TeX version (You will also need four figures for the Tex version. Figure 1, Figure 2, Figure 3, and Figure 4.) Or, Postscript version.

Project contributed by John Quintanilla.
This project gives some history of the computation of Pi. Students then are required to derive some of the formulas used.
Project teaches and provides practice in
• History of Pi
• Trigonometric identities
• Use of calculators or computers to approximate Pi