What This Document Is
This is a homework assignment designed for students enrolled in MATH 115: Preparation for Calculus at the University of Illinois at Urbana-Champaign. It focuses on foundational algebraic skills essential for success in calculus. The assignment is structured to reinforce understanding of core concepts through problem-solving practice. It’s intended to be completed individually as a means of self-assessment and preparation for more advanced coursework.
Why This Document Matters
This assignment is crucial for students who are building a strong base in algebra before tackling the complexities of calculus. Working through these types of problems will help solidify your understanding of essential techniques and identify areas where further review might be beneficial. It’s particularly helpful to complete this assignment *before* exams or quizzes, as it mirrors the types of questions you can expect to encounter. Students who consistently practice these skills will find themselves better prepared for the rigorous demands of a calculus sequence.
Topics Covered
* Solving Linear Equations (single variable)
* Solving for a Specific Variable within a Formula
* Word Problem Application (translating scenarios into algebraic expressions)
* Linear Inequalities (solving and interval notation)
* Absolute Value Equations and Inequalities
* Simplifying Expressions with Absolute Values
* Exponents and Algebraic Manipulation
What This Document Provides
* A series of practice problems designed to test algebraic proficiency.
* Problems requiring the application of multiple algebraic techniques.
* Opportunities to practice representing real-world scenarios mathematically.
* Exercises focused on understanding and utilizing interval notation.
* A range of problem types, from straightforward equation solving to more complex absolute value manipulations.
* Problems designed to reinforce the rules of exponents.
