What This Document Is
This is a focused activity designed to reinforce key concepts from the Preparation for Calculus (MATH 115) course at the University of Illinois at Urbana-Champaign. Specifically, it’s a group activity centered around polynomial functions and related problem-solving techniques. It’s intended to be completed collaboratively, building both individual understanding and teamwork skills. This resource provides a series of exercises to deepen your grasp of foundational algebraic principles essential for success in calculus.
Why This Document Matters
This activity is ideal for students currently enrolled in MATH 115 who are looking for extra practice and a collaborative learning experience. It’s particularly beneficial when working with peers to solidify understanding of polynomial manipulation and analysis. Use this resource to test your ability to apply concepts learned in lectures and readings to a variety of practical problems. Working through these types of exercises will build confidence and prepare you for more advanced coursework.
Topics Covered
* Polynomial Function Analysis (long-run behavior, intercepts)
* Solving Polynomial Equations
* Optimization Problems (finding maximum/minimum values)
* Polynomial Factoring and Zeros
* Polynomial Division
* Constructing Polynomials from Zeros
* Rational Root Theorem
* Intersection of Functions
What This Document Provides
* A series of practice problems designed to be tackled in a group setting.
* Exercises involving real-world applications of polynomial functions, such as cost analysis in a business scenario.
* Opportunities to practice identifying key features of polynomial graphs.
* Problems requiring the application of polynomial division techniques.
* A challenge question extending the concepts presented in the main activity.
* A framework for collaborative problem-solving and discussion of mathematical concepts.
