What This Document Is
This is an activity sheet designed to reinforce foundational concepts in Calculus (MATH 220) at the University of Illinois at Urbana-Champaign. It serves as a practice resource, helping students build proficiency in essential algebraic manipulations and pre-calculus skills necessary for success in the course. The sheet is structured as a series of problems and conceptual questions, intended to be worked through actively.
Why This Document Matters
This resource is particularly valuable for students who are reviewing prerequisite material or seeking extra practice with core algebraic techniques. It’s ideal for use during self-study, as a supplement to lectures, or as preparation for more advanced calculus topics. Students who feel less confident in their foundational skills will find this sheet especially helpful in solidifying their understanding and identifying areas where they may need further review. Access to the complete activity sheet unlocks detailed practice opportunities to strengthen your calculus readiness.
Topics Covered
* Algebraic Expressions & Simplification
* Factoring Techniques
* Equation Solving (including absolute value and quadratic equations)
* Domain of Functions (including square root functions)
* Function Definition & Representation
* Trigonometric Functions & Evaluation
* Interval Notation
What This Document Provides
* A series of problems designed to test understanding of fundamental algebraic principles.
* Opportunities to practice simplifying complex expressions.
* Exercises focused on determining the valid input values (domain) for various functions.
* Conceptual questions prompting reflection on the definition of a function and related tests.
* Practice with evaluating trigonometric functions at specific values.
* A starting point for building a strong foundation in the mathematical skills required for Calculus.
