## Course Exams

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

### Exam 1: Friday March 8 (in class)

Topics: Chapter 1 (excluding 1.7) and Sections 2.1 - 2.5.

In particular, you should be comfortable with the following:

• Functions Graph simple functions. Know what domain, range, image, even, odd, increasing and decreasing are.
• Limits 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.
• Derivatives Be able to state the definition of the derivative, as well as compute the derivative using limits. State the various differentiation rules (sum, product, quotient, chain) in either Leibnitz notation (df/dx) or prime notation (f'(x)). Use differentiation rules to differentiate functions. Graph the derivative of a function. Find the tangent line to a curve at a point. Understand how position and velocity are related to functions and their derivatives.

Practice problems I suggest you begin by reviewing your old homeworks and lecture notes, in particular the examples. One you feel moderately comfortable with your ability, you should try many practice problems. I cannot overemphasize the importance of making sure you can do these on your own (which means, you need to do them on your own). After solving practice problems, check your answers against the solutions to make sure you were correct. Bring any questions you may have to lecture, your discussion section, office hours and/or the Help Center. Some suggested practice problems from the text 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 (pp 93-96)
Concept Check: 1, 3, 7, 8
True-False Quiz: 1, 3, 5, 6, 8, 12, 15, 16, 17, 18, 23, 24, 25
Exercises: 23, 24, 25, 27, 32
• Chapter 2 Exercises
Section 2.3: 13, 17, 21
Section 2.4: 5, 11, 17, 21
Section 2.5: 1, 3, 7, 31, 41
• Chapter 2 Review (pp 190-193)
Concept Check: 4, 5, 6, 9
True-False Quiz: 1 - 9
Exercises: 1, 2, 3, 4, 5, 11, 13, 15, 17

Solutions to selected problems are now available under the "Content" section in the D2L page.

### Exam 2: Friday April 19 (in class)

Topics: Exam 2 will focus on Sections 2.3 - 2.8, Sections 3.1 - 3.3 and parts of 3.5, though you should still be familiar with earlier material. Specifically, you should be comfortable with the following:
• State the various differentiation rules (sum, product, quotient, chain) in either Leibnitz notation (df/dx) or prime notation (f'(x)).
• 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)
• 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
• Find vertical asymptotes
• Graph the derivative of a function
• Graph polynomials on the real line, and other functions on closed intervals
• Understand Rolle's Theorem and Mean Value Theorem

Suggestions: my suggestions for preparing are the same as for Exam 1. Here is a list of practice problems.

• Chapter 2 Review (pp 190-193)
Concept Check: 8, 9, 10, 11
True-False Quiz: 3-8, 10
Exercises: 15, 17, 19, 27, 33, 35, 37, 73(a)(b), 77, 79
• Chapter 3 Problems
Section 3.1: 11, 13
Section 3.3: 2, 3, 6, 7, 9, 11, 13, 15, 21, 27, 31, 41
• Chapter 3 Review (pp 275-278))
Concept Check: 1, 2, 3, 4, 5, 6
True-False Quiz: 1 - 8 (removed 9 and 10)
Exercises: 1, 5, 16, 17, 19

Solutions to selected problems are now available under the "Content" section in the D2L page. 4/17: Corrected Solution to 3.3:6.

### Final Exam: Wednesday May 8, 8-10am

The final exam will be cumulative. Specifically, it will cover Chapter 1 (excluding 1.7), Chapter 2 (excluding 2.9) and Chapter 3 (excluding 3.6 and 3.8). I recommend you prepare by going over your previous exams (and if possible alternate versions) and making sure you can do all problems correctly (on your own). I anticipate least 2/3 of the final exam will comprise questions similar to those on Exams 1 and 2. You should also do many practice problems (particularly those on Sections 3.4, 3.5, 3.7 and 3.9), which you can select from, the review problems listed below, your homework, or from additional problems/examples in the text.

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

• A variety of true/false
• Compute limits
• Compute the derivative of a simple function from the definition
• Compute the derivative of combinations of algebraic and trigonometric functions
• Find a tangent line to a curve (possibly using implicit differentiation)
• Given a position function, find velocity and acceleration
• Given velocity or acceleration and initial conditions, find the position function (or find a general antiderivative)
• A related rates problem
• Find local/absolute minima/maxima on an interval
• Find vertical and horizontal asymptotes
• Graph functions (in the style of the last problem on Exam 2, but likely for more complicated functions---maybe rational or algebraic 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, as on previous exams, there may be other topics/types of problems covered, such as "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)/vert asymptote at x=3/etc.]", or "Prove [d/dx tan x = sec^2 x/etc.]".

#### Final Review Practice Problems

• Chapter 1 Review (pp 93-96)
Concept Check: 1, 3, 4, 6, 8, 12, 13, 15(a)(d)(e), 16, 17, 18
True-False Quiz: all except 21
Exercises: 1, 12, 14, 15, 24, 25, 27, 29, 31
• Chapter 2 Review (pp 190-193)
Concept Check: 1, 2, 5, 6, 8(a)(b)(c)(e)(g), 9, 10
True-False Quiz: all
Exercises: 2, 3, 10, 11, 13, 14, 15, 16, 17, 20, 21, 23, 26, 33, 39
• Chapter 3 Review (pp 275-278)
Concept Check: 1, 2, 3, 4, 5, 6, 7, 10
True-False Quiz: 1-10, 18, 19
Exercises: 2, 7, 9, 10, 15, 18, 19, 20, 38
• In-section Exercises
Section 1.6: 44
Section 2.8: 12, 15, 17
Section 3.5: 9, 11, 25
Section 3.7: 15, 16, 19
Section 3.9: 1, 3, 51, 53

Solutions to selected problems are available under the "Content" section in the D2L course page.

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