# Math 122: Chapter 10 Exam Study Guide

- Convert the rectangular equation into polar form. Solve for
*r* or *r*^{2} if possible. (5 parts)
- Convert the polar equation into rectangular form. (5 parts)
- Find the rectangular equation of the described parabola.
- Write the polar equation of the graphed relation. These could involve roses, lemniscates, limaçons, cardiods, circles, ellipses, hyperbolas, parabolas, lines, and spirals. (12 parts)
- You are given a parametrically defined curve on an interval.
- Find dy/dx
- Find the equation of the line tangent to the curve at the indicated point.
- Find the length of the curve.

- You are given an equation in polar form.
- Find the derivative dy/dx.
- Find the length of the curve.
- Find the area enclosed by the curve.
- Find the area of the surfaced generated when a portion of the curve is rotated about the polar axis.
- Find the area of the surfaced generated when a portion of the curve is rotated about the θ = π/2 axis.

- Find the rectangular equation of the described hyperbola.
- Find the rectangular equation of the described ellipse.
- Find the polar equation for the described conic with a focus at the pole. (3 parts)

## Notes

- For problems requiring integration, first write the appropriate integral and then use the numeric integration feature of your calculator to approximate the value.
- There is a take home exam worth 40 points. It is due the day of the regular exam.
- There is a page to help with the LORAN-C problem on the take home.
- There are 104 possible points, which means that you can miss 4 points without hurting your grade.
- Bring a printed copy of your technology project with you if you would like to use it on the exam.

## Points per problem

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
Take Home |
Total |

Pts |
5 |
5 |
3 |
12 |
9 |
15 |
3 |
3 |
9 |
40 |
104 |