## Final II - Study Guide

1. Sketch the graph of a rational function. Pay attention to horizontal and vertical asymptotes, x-intercepts, holes, multiplicity of factors (odd/even).
2. Maximize a linear programming problem.
3. Consider a fourth degree polynomial function.
• Determine the possible number of positive, negative, and complex solutions.
• List all possible rational zeros of the function.
• Find all zeros of the function.
• Completely factor using linear and irreducible quadratic factors
4. Find the partial fraction decomposition of a rational function.
5. Write a polynomial function which matches the description given.
6. Write a rational function which matches the description given.
7. Write a conic section in standard form. No need to graph.
8. Work a variation problem (emphasis on Hooke's law).
9. Identify the conic section or degenerate case. Nine parts, no answer is duplicated. The possible answers are not listed.
10. Work a problem involving a geometric series.
11. Find the equation of a parabola passing through three points.
13. Multiply two matrices.
14. Find the inverse of a matrix.
15. Find the determinant of a matrix.
16. Multiply a scalar and a matrix.
17. Find the sum of an arithmetic sequence.
18. Write a function which has the given zeros.
19. Find the inverse of a function.
20. Identify the rule, definition, or theorem stated or applicable. 8 parts. You should at least know ...
• Definition of absolute value
• Definition of adjoint (Transpose of matrix of cofactors)
• Definition of break-even point
• Definition of combination
• Definition of circle
• Definition of ellipse
• Definition of factorial
• Definition of hyperbola
• Definition of inverse of a matrix (Adjoint divided by determinant)
• Definition of parabola
• Definition of permuation
• Descarte's rule of signs
• Fundamental theorem of algebra
• Fundamental theorem of arithmetic
• Fundamental theorem of linear programming.
21. Identify each statement as true or false. 8 parts. You should know at least ...
• Three elementary row operations that produce row-equivalent matrices.
• Four requirements of being in reduced echelon form.
• Three properties of logarithms involvings sums/products, differences/quotients, exponents/multiples.
• Associativity and commutativity of matrix addition and multiplication.
• The change of base formula for logarithms.
• Shortcuts for evaluating determinants of matrices.
• When the inverse of a matrix exists.
• The limit defintion of e.
• Definition of one-to-one function.
This exam is from 10:00 - 11:50 am on Monday. You may use your notebooks during this exam. Your notebooks may contain old exams, homework, and notes.

I strongly urge you to go through and organize your notebook before taking the exam. Examples of things you can do to improve your grade on the exam include ...

• Place index tabs in the notebook at the sections mentioned above. If your notes are lacking in any of these areas, fill them in.
• Copy all definitions and true-false answers/properties onto one page at the beginning of the notebook.
• Correct problems on old exams that you missed and are going to re-appear on the final. Make sure you know why you missed them the first time.
• Answer as many questions as you can before you go to your notes. Once you go to your notes, your productivity will really decrease.
• Answer the problems you know how to do first. Don't let problem 1 freak you out. There is no rule which says that you must answer the questions in order.