## Math 116: Study Guide - Final Exam

1. Describe the basic graph by name and the translation. The basic graphs are given on the front cover of the text. Three parts.
2. Identify the conic section or degenerate case. Nine parts.
3. Find the inverse of a function.
4. Find the first seven terms of a sequence. Identify how the sequence is defined (general term, recursively). Name the sequence (arithmetic, geometric, ???)
5. Solve a system of equations by graphing.
6. Solve a system of equations by substitution.
7. Solve a system of equations by addition or elimination.
8. Solve a system of equations by Cramer's Rule.
9. Solve a system of equations by Gauss Jordan Elimination
10. Solve a system of equations by Matrix Algebra.
11. Evaluate the difference quotient.
12. Find a function with the indicated zeros.
13. Maximize an objective function subject to the constraints.
14. Setup and solve a system of linear equations which will find the equation of a parabola passing through the given points. I suggest using matrix inverses to find the solution.
15. Multiply two matrices.
16. Find the inverse of a matrix.
17. Find the determinant of a matrix. The vertical lines do not mean take the absolute value.
18. Given a fourth degree polynomial function, give the total number of real or complex zeros, the maximum number of positive and negative roots, list all possible rational zeros, find all real or complex zeros, and completely factor the polynomial function using linear and irreducible quadratic factors.
19. Sketch a rational function.
20. Find a partial fraction decomposition.
21. Sketch a conic section in standard form.
22. Solve a logarithmic equation.
23. Solve a matrix equation.
24. Write whether or not the simplification is valid. If the simplification is invalid, then correct the right hand side or explain why the simplification is invalid. Seventeen parts. Capital letters represent matrices and lower case letters represent real numbers. Several of these deal with inverses (when do two things inverse out).
25. Identify the term, rule, or theorem defined, or which is applicable. You should know the following: Fundamental Theorem of Arithmetic, Fundamental Theorem of Algebra, Fundamental Theorem of Linear Programming, Fundamental Counting Principle, Descartes' Rule of Signs, Rational Root Theorem.; Definitions of circle, ellipse, parabola, hyperbola, combination, permutation. Eight parts.
26. Identify each statement as true or false. Concentrate on: Elementary row operations, Matrix multiplication, Melodic properties of logs, Determinants of special matrices, Relationship of a matrix inverse to its determinant, Relationship of a matrix inverse to its size, Limit definition of e, One-to-one functions in regards to line tests, Matrix division. Nine parts.

### Notes:

• Make sure you use the proper technique to solve the systems of equations. All the systems are 2x2.
• This test is open notebook. Your old tests may be in your notebook. This study guide should certainly be in the notebook.
• For the terms, rules, and/or theorems, write them all out on one piece of paper and stick that in your notebook so you don't have to go looking for things.
• Make sure your notes on the areas covered on the test are full. If you're notes aren't complete, supplement.
• You may want to organize your notes - perhaps index the sections with tabs that will be used on the test. Another idea would be to put all the notes for the test on at the beginning. Indexing would be better, as you may not get everything that's on the test, and then your notes would be out of order.
• Answer as many questions as you can without using your notes. You will not have adequate time to research every question in your notes.