Pre-calculus math principles come in a wide variety. Pre-calculus principles give fundamental understanding of nearly every math concept prior to calculus-based mathematics. Projects for pre-calculus range from trigonometry in art to parametric projects. They explore math-based principles and help students visualise the pre-calculus concepts. Successful pre-calculus projects require many hours of work and studying to display complex mathematical principles to a general audience.

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## Trigonometry Art

Trigonometry becomes beautiful with this pre-calculus project. The simplicity of this project involves a graphing calculator and a conventional means to graph trigonometric functions. Have students design this art with three different trigonometric functions and other types of functions, like polynomials. Require a certain area of picture, domain and range be coloured certain colours. This makes a great project restriction. Also allow other colours to help the aesthetics of the trigonometric art work.

## Parametric Relationships to Reality

This pre-calculus project requires knowledge of conic and motion equations. The only material is a graphing calculator and ample time to complete --- approximately two weeks. The first part requires students to describe physical phenomena, like a falling basketball. The second part requires students to convert between rectangular and parametric equations. This allows the equations to be graphed both conventionally and with a calculator. The last part of this project for pre-calculus, using earlier equations to determine other similar physical phenomena and their equations.

## Financing My First Car

Many pre-calculus students need this project. The formatting requires a list of questions to help determine the variables used in financing equations. Providing the equations and working an example helps student perform this project. Ask the questions needed to fill in equations, such as "What is the interest rate for your bank account?" Have students make their projects based on numbers they provide. (See the example in Resources for some suggestions.) This project is flexible, so get creative.

## Building Icosahedrons

This pre-calculus project requires patience and an understanding of surface area and volumes of geometric shapes. The icosahedron needs 20 equilateral triangles. They must be cut out individually and glued in to place. Rate the projects on performance and research for this model. For more guidance, require project problems, such as "Calculate the surface area and volume." This project can be guided as little or as much as desired.