Unit 9: Parametric, Polar & Vector-Valued Functions
Calculus BC · Unit 9 · Paper 1

Parametric, Polar & Vector-Valued Functions unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Paper 1Paper 2Paper 3
Each paper is built from this unit’s 34 terms and is the same for everyone, so a teacher can assign “Unit 9, Paper 1” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.
Suggested time 36 min 33 points0/17 attempted
1

Vector-valued position from velocity

2

Parametric second derivative

3

Distance equals the integral of speed

4

Area in polar coordinates

5

Displacement versus distance

6

Polar dy/dx

7

Petal width

8

Polar derivative dy/dx

9

Vertical and horizontal tangents parametrically

10

Acceleration vector

11

Parametric equations describe motion, not just a curve

12

Polar area is built from sectors

Short answer 1. Define or explain: Parametric horizontal tangent

3 pts

Short answer 2. Define or explain: Area between polar curves

3 pts

Short answer 3. Define or explain: Finding the limits for a polar area

3 pts

Short answer 4. Define or explain: Speeding up in the plane

3 pts

Free response

9 pts

CALCULATOR PERMITTED. The polar curve C is defined by r(θ) = 3 + 2 sin θ for 0 ≤ θ ≤ 2π. The circle r = 4 is also graphed in the xy-plane. (Your calculator should be in radian mode.)

A. Find the area of the region enclosed by curve C. Show the setup for your calculations.

B. Find the rate of change of r with respect to θ at θ = π/6. Show the setup for your calculations.

C. Find the area of the region that lies inside curve C and outside the circle r = 4. Show the setup for your calculations.

D. A particle travels along curve C so that dθ/dt = 3 for all times t. Find the rate at which the particle’s distance from the origin is changing when the particle is at the point where θ = π/6.