# Math 122: Chapter 10 Exam Study Guide

1. Convert the rectangular equation into polar form. Solve for r or r2 if possible. (5 parts)
2. Convert the polar equation into rectangular form. (5 parts)
3. Find the rectangular equation of the described parabola.
4. Write the polar equation of the graphed relation. These could involve roses, lemniscates, limaçons, cardiods, circles, ellipses, hyperbolas, parabolas, lines, and spirals. (12 parts)
5. You are given a parametrically defined curve on an interval.
1. Find dy/dx
2. Find the equation of the line tangent to the curve at the indicated point.
3. Find the length of the curve.
6. You are given an equation in polar form.
1. Find the derivative dy/dx.
2. Find the length of the curve.
3. Find the area enclosed by the curve.
4. Find the area of the surfaced generated when a portion of the curve is rotated about the polar axis.
5. Find the area of the surfaced generated when a portion of the curve is rotated about the θ = π/2 axis.
7. Find the rectangular equation of the described hyperbola.
8. Find the rectangular equation of the described ellipse.
9. 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

 # Pts 1 2 3 4 5 6 7 8 9 Take Home Total 5 5 3 12 9 15 3 3 9 40 104