What This Document Is
This document contains worked solutions to all problems from the first midterm exam for MIT’s 18.01 Calculus course, Fall 2021. It covers foundational calculus concepts assessed early in the semester. The exam was designed to be completed in two hours, without the use of books, notes, or calculators.
Why This Document Matters
This resource is primarily valuable for students who took the 18.01 Calculus course in Fall 2021, or for students currently studying the same material who want to test their understanding. It’s particularly useful for identifying common errors and understanding the expected level of rigor in problem-solving. It serves as a check on self-study and preparation.
Common Limitations or Challenges
This document provides *solutions* to specific problems, but it does not offer detailed explanations of the underlying calculus principles. It won’t teach you *how* to solve these types of problems, only what the correct answers are. Users still need a textbook, lecture notes, and practice to fully grasp the concepts. It is also specific to one particular exam and may not reflect all possible problem variations.
What This Document Provides
The full document includes complete, step-by-step solutions for:
* Four “finger exercises” covering basic differentiation and integration techniques (product rule, chain rule, integration by parts, u-substitution).
* Solutions related to graphing a polynomial function, including finding derivatives, identifying intervals of increase/decrease, and locating maxima.
* A detailed optimization problem involving the circumferences and areas of two circles.
* The complete exam questions are included as context for each solution.
This preview does *not* include the original exam questions themselves, nor does it provide any explanations beyond identifying the topics covered. It does not offer alternative solution methods or detailed justifications for each step.