What This Document Is
This is a past midterm examination for Math 128, Calculus II, offered at Washington University in St. Louis. It assesses understanding of core concepts typically covered in the early stages of a second calculus course, focusing on multivariable calculus. The exam is designed to evaluate a student’s ability to apply calculus principles to functions of multiple variables and to solve related optimization problems. It’s a closed-book exam allowing only a simple calculator and a small reference card.
Why This Document Matters
This resource is invaluable for students currently enrolled in Calculus II, or those preparing to take the course. It provides a realistic assessment of the types of questions and the level of difficulty expected on a midterm exam. Working through practice problems – and reviewing a completed exam like this one – is a highly effective study strategy. It’s particularly useful for identifying knowledge gaps and strengthening areas where you feel less confident. Students aiming for a strong grasp of partial derivatives, optimization, and constrained optimization will find this especially helpful.
Common Limitations or Challenges
This document presents a completed exam, but does *not* include detailed solutions or explanations. It serves as a practice tool for self-assessment, requiring you to independently apply your knowledge to solve the problems. It also represents a specific instance of a midterm from a prior semester; while indicative of the course material, future exams may vary in specific problem selection and emphasis. It does not cover all possible topics within Calculus II.
What This Document Provides
* A full set of exam questions covering topics such as partial derivatives.
* Problems requiring the analysis of functions of multiple variables.
* Questions focused on finding critical points and classifying them (maxima, minima, saddle points).
* Application problems involving optimization of profit functions.
* Problems utilizing the method of Lagrange multipliers for constrained optimization.
* Questions assessing understanding of tangent lines and cross-sectional analysis of functions.
* A clear indication of the exam format and allowed resources.
