Unit 4 practice



1.
Match the equation with its graph.

A.


B.


C.


D.


E.




2.
Sketch the curve represented by the parametric equations, and write the corresponding rectangular equation by eliminating the parameter.

A.

B.

C.

D.

E.
None of the above.


3.
Find .

A.
B.
C.
D.
E.


4.
For the given point in rectangular coordinates, find two sets of polar coordinates for the point for .

A.
B.
C.
D.
E.


5.
Find the area of the surface formed by revolving about the axis the following curve over the given interval.

A.
B.
C.
D.
E.


6.
Find the vertex, focus, and directrix of the parabola and sketch its graph.

A.
Vertex: (2,–4); Focus: (1,–4); Directrix x = 3

B.
Vertex: (2,–4); Focus: (1,–4); Directrix x = 3

C.
Vertex: (–2,4); Focus: (–3,–4); Directrix x = –1

D.
Vertex: (–2,4); Focus: (–3,–4); Directrix x = –1

E.
Vertex: (2,–4); Focus: (3,–4); Directrix x = 1



7.
Find an equation of the ellipse with vertices (0,2), (16,2) and eccentricity .
A.
B.
C.
D.
E.


8.
Sketch the curve represented by the parametric equations, and write the corresponding rectangular equation by eliminating the parameter.

A.

B.

C.

D.

E.



9.
Find the arc length of the curve on the given interval.

A.
B.
C.
D.
E.


10.
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)


11.
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)


12.
For the given point in polar coordinates, find the corresponding rectangular coordinates for the point.

A.
(,12)
B.
(0,–6)
C.
(0,6)
D.
(,–12)
E.
(0,12)


13.
Match the graph with its polar equation.

A.
B.
C.
D.
E.


14.
Convert the rectangular equation to polar form.

A.

B.

C.

D.

E.



15.
Find the points of intersection of the graphs of the equations.

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


16.
Find the length of the curve over the given interval.

A.
B.
C.
D.
E.


17.
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.



STOP This is the end of the test. When you have completed all the questions and reviewed your answers, press the button below to grade the test.