March 2, 2019
This test contains 10 short answer questions. All answers must be expressed in
simplest form unless specified otherwise. Only answers written inside the boxes on the answer
sheet will be considered for grading.
(0) = 100.
2. Farmer Joe will plant carrots to cover a rectangle in the first quadrant with a vertex at
the origin and sides parallel to the
However, he can not grow carrots on
his neighbor’s land.
If the border between his and his neighbor’s land is along the curve
), what is the maximum area of carrotland Farmer Joe can create?
3. For all
from 0 to 2
, Annie draws a line segment of length
from the origin in the direction
radians. What is the area of the spiral swept out by the union of these line segments?