What This Document Is
This document is a past exam – specifically, Test 3 – from a Calculus I course (MATH 221) at the University of Illinois at Urbana-Champaign, administered in 2012. It’s designed to assess your understanding of key concepts and problem-solving abilities related to integral calculus and its applications. This is a valuable resource for students preparing for their own Calculus I assessments.
Why This Document Matters
If you are currently enrolled in Calculus I, or are reviewing the material for an upcoming exam, this resource can be incredibly helpful. Working through past exams allows you to familiarize yourself with the typical question formats, the level of difficulty expected, and the types of problems your instructor might present. It’s an excellent way to test your knowledge, identify areas where you need further study, and build confidence before a high-stakes evaluation. Accessing the full test will allow you to practice under timed conditions, simulating the real exam experience.
Topics Covered
* Definite and Indefinite Integrals
* Fundamental Theorem of Calculus
* Riemann Sums and Limits
* Applications of Integration – Area between curves
* Volumes of Solids of Revolution (Disk/Washer & Shell Methods)
* Applications of Integration – Work
* Optimization Problems (Finding Minimum Values)
* Integration Techniques
* Properties of Integrals and related theorems
* The relationship between differentiation and integration
What This Document Provides
* A complete, previously administered Calculus I exam.
* A variety of problem types covering core integration concepts.
* Questions requiring both computational skills and conceptual understanding.
* Problems involving geometric applications of integration, such as finding areas and volumes.
* Opportunities to practice applying calculus to real-world scenarios, like calculating work done in pumping fluids.
* A selection of questions designed to test your understanding of the connections between derivatives and integrals.
* Short answer questions to assess your grasp of fundamental theorems and definitions.
