Chapter 10 Practice Test - AP Calculus BC
Chapter 10 Practice Test (On-line)



1.
Find the vertex, focus, and directrix of the parabola and sketch its graph.

A.
Vertex: (2,–3); Focus: (1,–3); Directrix x = 3
B.
Vertex: (2,–3); Focus: (1,–3); Directrix x = 3
C.
Vertex: (–2,3); Focus: (–3,–3); Directrix x = –1
D.
Vertex: (–2,3); Focus: (–3,–3); Directrix x = –1
E.
Vertex: (2,–3); Focus: (3,–3); Directrix x = 1


2.
Find the center, foci, vertices, and eccentricity of the ellipse. (The equation may not be in this form.)

A.
Center: (2,–4); Vertices: (–3,–4) , (7,–4); Foci: (2,–8) , (6,0); Eccentricity:
B.
Center: (2,–4); Vertices: (2,–9) , (2,1); Foci: (2,–8) , (2,0); Eccentricity:
C.
Center: (2,–4); Vertices: (–3,–4) , (7,–4); Foci: (–2,–4) , (6,–4); Eccentricity:
D.
Center: (2,–4); Vertices: (–3,–4) , (7,–4); Foci: (–2,–4) , (6,–4); Eccentricity:
E.
Center: (2,–4); Vertices: (–3,–4) , (7,–4); Foci: (–2,–4) , (6,–4); Eccentricity:


3.
Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

A.
Parabola
B.
Circle
C.
Ellipse
D.
Hyperbola


4.
Find .

A.
B.
C.
D.
E.
None of the above


5.
Find and if possible, and find the slope and concavity (if possible) at the point corresponding to t = 1.

A.
. At t = 1: slope 8 and concave up
B.
. At t = 1: slope 4 and concave down
C.
. At t = 1: slope and concave up
D.
. At t = 1: slope –4 and concave down
E.
. At t = 1: slope and concave up


6.
Find the arc length of the curve on the given interval.

A.
B.
C.
D.
E.


7.
Find the area of the surface generated by revolving the curve about the given axis.



(i) x-axis; (ii) y-axis
A.
(i) ; (ii)
B.
(i) ; (ii)
C.
(i) ; (ii)
D.
(i) ; (ii)
E.
(i) ; (ii)


8.
Convert the rectangular equation to polar form.

A.

B.

C.

D.

E.



9.
Find the length of the curve over the given interval.

A.
B.
C.
D.
E.


10.
Find the area of the surface formed by revolving about the polar axis the following curve over the given interval.

A.
B.
C.
D.
E.


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