Math 242C

Midterm Exam 1 Review Sheet

Practice exams

Here are some exams I have given in the past years covering roughly the same material. There are some differences in both the syllabus and in the notation and terminology, since some of the earlier exams were based on a different text (by Stewart) or a different edition of the Edwards/Penney text we are using now. In particular, you can ignore questions on the following topics, which were covered in the Stewart text, but are not covered in Edwards/Penney (or, in some cases, buried in the excercise sections), and which we didn't go over in class, or have problems on: Also note that some of the earlier exams used the term "orthogonal" rather than "perpendicular". Orthogonal means exactly the same thing as perpendicular (as does the term "normal" when used in this context). Finally, note that 11.7 (quadratic surfaces) is included in our syllabus, but not 11.8 (cylindrical/spherical coordinates). Thus you can ignore questions about the latter (11.8), but you should be prepared for questions on quadratic surfaces (of the same type as the hw problems on this section and the problems discussed in Thursday's (9/21) recitation sections).

In terms of the difficulty level and nature of the problems, these exams are pretty representative of what you can expect in our exam.

General Information

Exam content

The exam will cover Sections 11.1-11.7, except for those parts that have not been covered in class and are explicitly marked in the lecture summaries as material that can be skipped. I expect to have covered all of this material by Wednesday, September 20, one week before the exam date. (Section 11.8 on cylindrical/spherical coordinates will be deferred until the beginning of Chapter 13. I will begin Chapter 12 on Monday, 9/25, but this material will not be on the exam.)

There will be no limit problems and no problems asking to sketch a curve or a surface.

The majority of the exam problems will be comparable to an average homework problem (and above the level of a typical quiz problem), and fall into one of the types listed below under "Typical Tasks." One or two problems will be somewhat less routine, comparable to some of the more difficult homework problems. Some questions may be in multiple choice or true/false format. The practice exams above will give you a good idea of what to expect.

Grading

Tips on preparing for the exam

Concepts and Formulas

As a first step in preparing for the exam you should review the concepts and formulas that we have discussed in class. The following is a list of things that you should be familiar with. Go through that list item by item; if you are a bit fuzzy about a concept or unsure about a formula, review the material from your class notes and the appropriate sections in the book, and practice it by working some problems (from the assigned hw problems or examples (from the list of suggested examples included with the lecture summaries).

An excellent idea is to use the list below to prepare a "cheat sheet" containing all formulas you need to know for the exam. Just looking up formulas in the book or in your lecture notes and writing those formulas down on a sheet of paper helps you committing those formulas to memory. Of course, you shouldn't bring these formulas to the exam.

11.1/11.2 Vectors

11.2 Dot products

11.3 Cross products

11.4 Lines and planes in space

11.5 Vector-valued functions and curves and motion in space

11.6 Curvature and acceleration

11.7: Quadratic surfaces

Typical tasks

11.1 - 11.3 Vectors, dot and cross products

11.4 Equations of lines and planes

11.5 Vector functions and space curves

11.6 Arc length, curvature, unit normal and unit tangent vectors, normal and tangential components of acceleration

11.7 Quadratic surfaces

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