Course Exams
Note: Information will be added as the exam dates near.
Exam 1: Mon Sep 27 (in class)
Exam 1 will cover the material in Sections 1.1, 1.2, 1.3, 2.1, 2.2, 2.3, 2.5
and 3.1. Some of the more important topics are:
- 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)
Topics.
Exam 2 will cover Chapter 3, excluding Section 3.9.
You should be able to do the following:
- 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)
Exam 3 is meant to give you exam practice on the material in Chapter 4
before the final exam. It will be graded, and recorded as your HW 12 grade.
This exam will cover the following sections: 4.1-4.5, 4.6, 4.7 and 4.9.
You should be able to do the following
- 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)
I recommend that you prepare by reviewing your homeworks, notes and doing
several practice problems. Here are some suggested practice problems
- 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
The final exam will cover all material listed above for Exams 1-3.
Therefore, you should be comfortable with all the topics listed above
for Exams 1-3.
I recommend you prepare by going over your previous exams and making sure you
can do all problems correctly (on your own). You should also do many practice
problems, which you can select from your homework, the review problems listed
above, or from additional problems/examples in the text.
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
While I have not made up the exam yet, I plan to place all of the above to be
on the exam.
In addition, there may be other topics/types of problems covered, such as
"Show ... has
exactly one root", "State the defintion of [continuity/derivative/vertical
asymptote/etc.]", "Graph a function with these properties ... [odd/jump
discontinuity at 0/continuous but not differentiable at 1, concave up on
(-1,0)/increasing on (0,1)/slant asymptote/etc.]", or
"Prove [the quotient rule from the chain rule and the product rule/the
derivative of an odd function is even/etc.]".
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