What This Document Is
This is a focused preparation resource designed to help students assess their understanding of key concepts covered in the first exam for Calculus I (MATH 221) at the University of Illinois at Urbana-Champaign. It’s structured as a ‘Key Prep’ guide, meaning it concentrates on essential skills and problem-solving techniques likely to appear on the assessment. This resource is intended to be used *in addition* to coursework materials, not as a replacement for them.
Why This Document Matters
This resource is ideal for students who want to proactively gauge their readiness for Exam 1A. It’s particularly beneficial for those seeking targeted practice in areas where they feel less confident, or for students who want to refine their approach to common Calculus I problem types. Utilizing this guide before the exam can help identify knowledge gaps and allow for focused review, ultimately boosting performance and reducing test-day anxiety. It’s best used after completing related coursework and practice problems.
Topics Covered
* Foundations of Functions and Graphs: Continuity and differentiability.
* Limits: Evaluating limits graphically and analytically.
* Applications of Functions: Modeling physical scenarios with graphs.
* Derivatives: Definition and application of derivative rules.
* Tangent Lines and Rates of Change: Finding equations of tangent lines.
* Asymptotes: Identifying horizontal and vertical asymptotes.
* Chain Rule and Related Differentiation Techniques.
* Composite Functions and their Derivatives.
* Parametric Curves and Area Calculations.
What This Document Provides
* A series of practice questions designed to mirror the style and difficulty of questions found on Exam 1A.
* Opportunities to apply core calculus concepts to various problem types.
* Exercises focused on interpreting graphical representations of functions and their derivatives.
* Problems requiring the application of the definition of the derivative.
* Practice with differentiating a variety of functions, including trigonometric and composite functions.
* A section dedicated to applying derivative rules to related rates problems.
* A challenging problem involving parametric curves and geometric area calculations.
* A table of values to practice applying the chain rule and related differentiation techniques.
