# Math 116 - Chapter 4 & 7 Study Guide

- Simplify the expressions involving logarithmic and exponential functions. Give exact values. For example log
_{4} 4^{1.7} = 1.7. Twelve parts.
- Identify the conic section or degenerate case. Choices are no graph,
point, line, parallel lines, intersecting lines, parabola, circle, ellipse,
and
hyperbola. Nine parts.
- Write the equation of the conic section. Three parts.
- Write the expression as a sum, difference, and/or constant multiple of
logarithms and simplify (if possible). Three parts.
- Write the expression as the logarithm of a single quantity. Three parts.
- Solve the equations. Give an exact answer (example, leave answer as ln 7 rather than going to the calculator to get a decimal approximation). Pay attention
to domain.
Four parts.
- Given a parametrically defined curve, complete a table of values and sketch the curve, indicating the direction of increasing t. Eliminate
the parameter and solve for y. Be sure to include any restrictions that
are necessary.
- Given the equation of a parabola, find the vertex, focus, and directrix. Sketch the graph.
- Given the equation of an ellipse, find the center, foci, and vertices. Sketch the graph.
- Given the equation of a hyperbola, find the center, foci, vertices, and asymptotes. Sketch the graph.
- Write the equation of the conic section in standard form. This will involve completing the square. Three parts.
- Identify the translation and give the domain and range of the translated graph.
- Analyze a polynomial function.
- Analyze a rational function.
- Write the equation of the graphed relation. Nine parts.

## Notes

- Questions 1 - 3 are to be done without a calculator. You may use a calculator for the rest of the exam.
- None of the problems on the test are straight from the text, but should
be similar to the problems in the text.
- There is a take-home portion of the exam worth 38 points and is due the day of the exam.
- The take-home portion has a web page to help you complete the LORAN-C Navigation problem.
- The LORAN-C problem on the take home test can be difficult if you don't
carefully read the instructions.

## Points per problem

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
Take
Home |
Total |

Pts |
24 |
9 |
12 |
9 |
9 |
16 |
5 |
8 |
8 |
8 |
12 |
9 |
9 |
6 |
18 |
38 |
200 |