Note: Information will be added as the exam dates near.

Exam 1: Mon Sep 27 (in class)

• Chapter 1. Graph simple functions. Know what domain, range, image, even and odd are. (Recall, our definition of range is different than the text's.) Be comfortable with polynomials, rational functions, trigonometric functions, algebraic functions and compositions.
• Chapter 2. Compute limits and determine when they don't exist. Be familiar with the limit laws (you need not remember them by number). Determine where a function is continuous/continuous. Be familiar with the basic types of discontinuities: removable, jump and infinite. Similarly, be familiar with left/right hand limits and left/right hand continuity. Squeeze Theorem. Intermediate Value Theorem.
• Chapter 3. Be able to state the definition of the derivative at a point, as well as compute the derivative at a point using limits. Find the tangent line to a curve at a point.

Warning. This is not necessarily a complete list of topics that will be covered on the exam, but what are in my mind the most important ones.

Format. The exam will be handed out to you with sufficient room to do work and write your answers. You should not need scratch paper. The only thing you will be allowed on your desk is your pencil/eraser. The exam will most likely consist of 3 sections: (1) True/False (no justification is needed), (2) Short Questions (only answer is required), (3) Problems (show your work).

Suggestions. I suggest you begin by reviewing your old homeworks and lecture notes, in particular the examples. The best way to prepare for the exam is to do practice problems. These can be found at the end of each section as well as in the Review sections at the end of each chapter. I suggest you do an ample selection of practice problems, and bring any questions you may have to lecture Friday, your recitation section, office hours and/or the Help Center. Suggested practice problems are listed below, though for specific topics you do not feel comfortable with, you should consider looking through the relevant section/notes for additional examples and problems.

• Chapter 1 Review
  Concept Check: 1, 3, 4, 6, 7, 8, 9, 10, 11
  True-False Quiz: 1-6
  Exercises: 11-17, 20
• Chapter 2 Review
  Concept Check: 1-7
  True-False Quiz: 1-10
  Exercises: 1-9, 15, 18, 23, 25, 27
• Section 3.1
  Exercises: 3(a-i,b), 5, 7, 25, 27

Exam 2: Mon Nov 1 (in class)

• State the definition of the derivative
• State the various differentiation rules (sum, product, quotient, chain) in either Leibnitz notation (df/dx) or prime notation (f'(x)).
• Calculate the derivative of a function using the definition
• Graph the derivative of a function
• Use differentiation rules to differentiate functions
• Differentiation equations implicitly
• Find equations of tangent lines
• Solve rates of change problems (e.g., velocity, acceleration)
• Solve related rates problems (given in words)

Format. The exam will be handed out to you with sufficient room to do work and write your answers. You should not need scratch paper. The only thing you will be allowed on your desk is your pencil/eraser. The exam will likely consist of 2 sections: (1) questions where only the answer is required, and (2) problems where you will be graded on your work.

Suggestions. I suggest you begin by reviewing your old homeworks and lecture notes, in particular the examples. The best way to prepare for the exam is to do practice problems. These can be found at the end of each section as well as in the Review sections at the end of each chapter. I suggest you do an ample selection of practice problems, and bring any questions you may have to lecture Friday, your recitation section, office hours and/or the Help Center. Suggested practice problems are listed below, though for specific topics you do not feel comfortable with, you should consider looking through the relevant section/notes for additional examples and problems. As much as possible, you should do practice problems on each topic until you are comfortable doing them on your own without any assistance (including the text or notes). It may be helpful to treat the practice problems below as a mock exam (there are many more questions here than would be on a 50-minute exam, but perhaps try a certain number on your own in a given period of time after studying).

• Chapter 3 Review Problems (pp. 196--199)
  Concept Check: 1-6, 8-10
  True-False Quiz: 1-6, 11, 12
  Exercises: 3-5, 10, 11, 13-20, 28, 29, 33, 35, 39, 47, 54, 72, 77-80
• Additional Exercises
  Section 3.3: 61, 71
  Section 3.4: 17, 20
  Section 3.5: 83, 84
  Section 3.6: 25, 27
  Section 3.8: 11-15

Exam 3: Mon Dec 6 (in class)

• Find local and absolute minima and maxima of functions (including the first and second derivative tests)
• Determine intervals of increase/decrease
• Determine concavity/inflection points
• Determine limits at infinity
• Find vertical, horizontal and slope asymptotes
• Graph functions
• Understand and use the Mean Value Theorem (e.g., to roots of equations)
• Solve optimization problems
• Find antiderivatives and apply this (e.g., determine a position function)

• Chapter 4 Review problems (pp. 281-284)
  Concept Check: 1, 2, 4, 5, 6, 7, 10
  True-False: all
  Exercises: 3, 4, 5, 8, 12, 13, 15, 19, 21, 23, 27, 33, 38, 40, 41, 46, 47, 53, 54, 56, 59, 60 (s is position)

Final Exam: Th Dec 16 1:30-3:30pm

You should at the least, expect the following on the final exam.

• A variety of true/false
• Compute limits
• Compute the derivative simple functions from the definition
• Compute the derivative of any combination of algebraic and trigonometric functions
• Find a tangent line to a curve using implicit differentiation
• Given a position function, find velocity and acceleration
• Given velocity or acceleration and initial conditions, find the position function
• A related rates problem
• Find local/absolute minima/maxima on an interval
• Find vertical, horizontal and slope asymptotes
• Graph functions (in the style of the last problem on Exam 3, but likely for more complicated functions---maybe rational or algebraic functions, or one involving trigonometric functions)
• An optimization problem