The final exam for Math Xa will be held on Saturday, Jan.13th from 9:15am to 12:15pm in Science Center D.

Review Schedules:
In addition to the reviews that your TF might have arranged for your section during the reading period, there will also be two coursewide reviews held on:
Tuesday, Jan. 9th, from 8pm to 9:30 in Science Center C, and
Thursday, Jan. 11th (also from 8pm to 9:30) in Science Center A.

Also, each of the TFs for the course will be hosting office hours during the week before the final, from Jan. 8th to Jan. 12th as follows.  You should feel free to stop by any of the TFs during their office hours to help you get ready for the final, not just your own TF's.  In addition, the Math Question Center will be running each evening from 8pm -10pm in Loker.

Monday, Jan 8th:
9am-11am, 12-5pm (room 506, Dale)
12pm - 1:30 (room 435, Andy)
8pm -10pm Math Question Center (Loker)

Tuesday, Jan 9th:
9am-11, 2:30-5pm (room 506, Dale)
4pm-5:30 (room 426b, Marty)
8pm -10pm Math Question Center (Loker)
8pm - 9:30 Coursewide Review (Science Center C)

Wednesday, Jan 10th:
9am-11, 12-5pm (room 506, Dale)
12pm - 1:30, 3-5 (room 435, Andy)
1pm-2:30 (room 321d, Laura)
4pm-5:30 (room 426b, Marty)
8pm -10pm Math Question Center (Loker)

Thursday, Jan 11th:
9am-11, 12-5pm (room 506, Dale)
1pm-2:30 (room 321d, Laura)
4pm-5:30 (room 426b, Marty)
8pm -10pm Math Question Center (Loker)
8pm - 9:30 Coursewide Review (Science Center A)

Friday, Jan 12th:
9am-11, 12-5pm (room 506, Dale)
12pm - 1:30, 3-5 (room 435, Andy)
1pm-2:30 (room 321d, Laura)
4pm-5:30 (room 426b, Marty)
8pm -10pm Math Question Center (Loker)
 

Topics for Final:
Topics for the final exam will cover all of the material from the semester.  As it is cumulative, you should expect that about 1/3rd of the test will cover material from the first part of the semester (up to the first midterm), 1/3rd will be on the material covered up to the second midterm, and 1/3rd will cover topics learned since the last midterm.  In terms of topics on the exam, the main topics we covered this semester are listed below.  To get ready for the final, you might consider finding homework or practice exam questions to test yourself on each of the various topics on this list.

• Functions
• Definition of a function (vertical line test)
• Graphing functions, reading graphs
• Know basic functions such as absolute value function
• Creating new functions
• Adding, multiplying and composing functions
• Altering graphs of functions by shifting, flipping and stretching
• Average rates of change
• Calculating values
• Interpreting meaning graphically
• Finding inverses of functions
• Solving for the output variable to calculate inverse functions
• Graphically inverting over y = x line
• Knowing when inverses exist (such as with horizontal line test)
• Specific Examples of Functions
• Linear functions
• Piecewise linear functions - formulas, applications
• Applications of linear functions for linear approximations
• Polynomial functions
• Basic characteristics
• Number, location of roots, turning points, inflection points
• Graphing polynomials
• Determining possible functions for particular graphs
• Rational functions
• Recognizing possible functions for rational function graphs
• Determining vertical and horizontal asymptotes
• Exponential functions
• Determining formulas
• Graphing exponential functions
• Exponential growth and decay applications
• Derivatives of exponential functions
• Logarithmic functions
• Definition as inverse functions for exponential functions
• Graphs of log functions
• Using logarithms and exponentials to solve equations
• Derivatives of logarithmic functions
• Limits
• Computing limits from graphs and functions
• Calculating left-hand, right-hand limits
• Continuity as defined with existence of limits
• Derivatives
• Basic definitions - derivative as instantaneous rate of change, slope of tangent line
• Calculating derivatives:
• Using limit definition of derivative
• Derivatives of polynomials, exponential and logarithmic functions
• Calculating derivatives analytically - using formulas:
• Product Rule
• Quotient Rule
• Power Rule
• Chain Rule
• Graphing first and second derivatives of a function given its graph
• Interpreting first and second derivatives (i.e. slope, concavity, respectively)
• Applications of derivatives
• Extrema
• Definition of critical points
• Finding minimum/maximums for functions
• Difference between local (relative) and global (absolute) extrema
• Optimization
• Setting up and solving optimization problems
• Testing min vs. max using first and second derivative tests

Final Exam from Fall 1999

Solution to Fall 1999

Final Exam from Fall 1998

Solution to Fall 1998

Final Exam from Fall 1997

Solution to Fall 1997
 

Finally, here are some review worksheets for you to use if you'd like to do a few more review problems!  There are three parts to the review sheets, as these were the same ones that Andy used in his three class reviews on MWF, Jan 8, 10 and 12th.  The answers are all written out on the last four pages of the review packet.

More Review Worksheets for the Final