BC Calculus 2012 Form Bpolars Non Calculator Name ______

BC Calculus 2012 Form BPolars Non calculator Name ______

1. Graph the point and name 3

other points which represents the same

location .

2. Convert to Cartesian coordinates / a Cartesian equation.

a. b. (Clear fractions and radicals)

3. Convert to polar coordinates/polar equation.

a) b. 4x – 5y = 6 (solve for r)

4. Multiple Choice. The graph of is symmetric to

I. the polar axis II. the line III. the pole

(A) I only (B) II only (C) I and II(D) II and III (E) I , II and III

5) Sketch the following curves.

a) r =─5cosθb)

6. Find all points of intersection of the curves r = 2 ─2 sin θ and r = ─6 sin θ.

7. (a) Sketch the curve and indicate this section.

(b)Set up the mathematics needed to find the length of this curve. (Do not simplify. Set up only!)

8. Find the arc length of the spiral between .

9. Find the values where the equation has (a) vertical tangent(s).

(Do not worry about checking if there is overlap with horizontal tangents: If you finish the entire test, you may come back and check for overlap with horizontal tangents for 2 bonus points. Please note: you are not eligible for these bonus points unless you finish the entire test first!).

10. Given , find the following.

(a) Find the slope of the tangent line to the polar curve at .

(b) Use the slope to find the equation of the tangent line at this point.

Show the calculus that leads to your answer. Show all work relating to polar curves!!

11. Sketch the graph. Find the area inside one petal of the rose r = 5cos(3). Show all work leading to the solution. (This problem is NOT set up only)

12. Sketch the graph, and set up leading to the solution tofind the area inside

the circle r = 3cos and outside the convex limacon r = 2─ cos. (Set up only).

AP Calculus Polar Equations2012 Form BName ______

Calculator allowed

13. a) Sketch the graphs.

b) Find points of intersection of these curves.

c) Set up the integral used to find the area inside both curves.

14. Giventhe limaςon : .

a) Find the area of the region inside the inner loop.

b) Find the length ofthe outer loop.

BC Calculus Polar Equations

Name ______

Take home:

Given the equation (Period = 2)

a) When is the graph at the pole?

b) Set up the integral to find the area of the two larger loops. (Use your calculator to evaluate.)

c) Set up the integral to find the length of one of the smaller loops.