What This Document Is
This document is a past examination paper for Calculus I (MATH 221) at the University of Illinois at Urbana-Champaign, specifically Test 2 from 2012. It represents a realistic assessment of the concepts and problem-solving skills taught within the course at that point in the semester. This resource offers a valuable opportunity to gauge your understanding of core calculus principles.
Why This Document Matters
This test is ideal for students currently enrolled in Calculus I, or those preparing to take the course. Working through past exams is a proven method for identifying knowledge gaps and becoming familiar with the types of questions and the level of difficulty expected. It’s particularly useful for focused practice before quizzes or larger exams, and can help build confidence in your ability to apply calculus techniques. Accessing the full test allows for a complete and authentic practice experience.
Topics Covered
* Limits and Continuity
* Derivatives and Applications (including related rates)
* Optimization Problems (absolute maximum and minimum values)
* Curve Sketching (using first and second derivatives)
* Exponential and Logarithmic Functions
* Applications of Derivatives to real-world scenarios
* Implicit Differentiation
* Analysis of Function Behavior (increasing/decreasing intervals, concavity)
What This Document Provides
* A full set of exam questions as they were originally presented to students.
* Problems requiring detailed solutions and justifications.
* A variety of question types, including theoretical problems and applied calculations.
* An opportunity to practice time management under exam conditions.
* Insight into the professor’s expectations regarding problem-solving approach and presentation of work.
* Questions designed to test conceptual understanding alongside computational skills.
