Math 116 - Final Exam Study Guide
- Six graphs from the eight basic graphs on the front
cover of the text, are shown. For each graph, identify the name of the basic
graph and the
equation of the graph shown.
- Find the inverse of a function.
- A table of x, f(x), and g(x) values is given. Use the table to find the
combination of functions. Five parts.
- Solve a equation for x.
- Simplify an expression involving i.
- Find a function with the indicated zeros. Pay special attention to
those involving radical or complex roots.
- Use synthetic division to divide a polynomial by a binomial.
- Given the sketch of a polynomial function, write a function (in factored
form) whose graph could be that shown.
- Given a polynomial function, give the total number of real or complex
zeros, the maximum number of positive and negative roots, the right and left
hand behavior of the graph, where the graph crosses and touches the x-axis,
the y-intercept, the domain, the form of any possible rational zeros, and
all real and complex roots.
- Given the sketch of a rational function, write a function (in factored
form) whose graph could be that shown.
- Given a rational function, give the domain, the behavior at a point where
there is a common factor between the numerator and denominator, the behavior
at each vertical asymptote and x-intercept, and the horizontal asymptote.
- Combine several logarithms into a single logarithm.
- Expand a single logarithm into the sum, difference, and constant multiples
of several logarithms.
- Solve the logarithmic equation.
- Find the partial fraction decomposition for the expression.
- Solve a system of linear equations by graphing.
- Solve a system of linear equations by substitution.
- Solve a system of linear equations by addition or elimination.
- Solve a system of linear equations by Gauss Jordan Elimination using
matrices.
- Solve a system of linear equations by Cramer's Rule.
- Solve a system of linear equations by Matrix Algebra. You can use the
calculator, but write the matrices entered into the calculator and the expression
evaluated
with the calculator.
- 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.
- Multiply two matrices.
- Find the inverse of a matrix.
- Find the determinant of a 3×3 matrix. The vertical lines do not mean
take the absolute value.
- Solve a matrix equation. Watch out for commutativity and division.
- Write the solution to a system of linear equations from a matrix in row
echelon form.
- Write the solution to a system of linear equations from a matrix in reduced
row echelon form.
- Write the first five terms of the sequence with the given general
term.
- Find the sum of an arithmetic series.
- Find the sum of an infinite geometric series.
- Simplify the ratio of the factorials.
- Expand a binomial using the binomial expansion theorem.
- Identify the conic section or degenerate case. Nine parts.
- Eliminate the parameter from a set of parametric equations.
- Sketch the graph of the conic section that is already in standard form.
- Complete
the square and place the conic section into standard form. Then sketch
the graph.
- Find the equation of the conic section shown.
- Write whether or not the simplification is valid. 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?).
Notes:
- Make sure you use the proper technique to solve the systems of equations.
All the systems are 2×2.
- This test is open notebook. Your old tests may be in your notebook.
This study guide should certainly be in the notebook.
- Make sure your notes on the areas covered on the test are full. If your
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. Some people like to take the study guide and indicate
what section
of the book that applies to so they know where to go in their notes.
- The test has been arranged so that it is is primarily in chapter 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.
Points per problem
| # |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| Pts |
12 |
4 |
5 |
4 |
4 |
4 |
4 |
4 |
11 |
4 |
| |
| # |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
| Pts |
6 |
4 |
4 |
4 |
5 |
5 |
5 |
5 |
5 |
5 |
| |
| # |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
| Pts |
5 |
5 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
| |
| # |
31 |
32 |
33 |
34 |
35 |
36 |
37 |
38 |
39 |
Total |
| Pts |
4 |
4 |
4 |
9 |
4 |
4 |
4 |
4 |
17 |
200 |