Question 1

Find a corresponding x-y equation.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 2

Find the area enclosed by the given curve.

Accepted Answer

A)    
B)  0 
C)    
D)    
A)    
B)  0 
C)    
D)

Question 3

At time t = 0 seconds, a hockey puck is headed towards the "board" (the wall around the perimeter of the area of play) as shown in the figure (the view is from above the playing surface). At that same instant, a hockey player at a different position on the ice is headed straight up the ice in order to intercept the puck (see figure). The trajectories of the puck and the player are described by the following set of parametric equations:   Find the location(s) of intersection of the trajectories of the player and the puck. Distances are in feet and time is in seconds.   [figure is not necessarily drawn to scale]

Accepted Answer

A)    and   
B)    
C)    and   
D)    
A)    and   
B)    
C)    and   
D)

Question 4

Identify a range of values of   that produces one copy of the graph.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 5

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

Find all points of intersection of the two curves.

Accepted Answer

A)    
B)    
C)    
D)  The curves have no point of intersection. 
A)    
B)    
C)    
D)  The curves have no point of intersection.

Question 7

A medical procedure called shockwave lithotripsy is used to break up kidney stones that are too large or irregular to be passed. In this procedure, shockwaves emanating from a transducer located at the other focus. Suppose that the reflector is described by the equation   (in units of inches), how far from the kidney stone should the transducer be placed?

Accepted Answer

A)  9 in. 
B)  81 in. 
C)  11 in. 
D)  13 in. 
A)  9 in. 
B)  81 in. 
C)  11 in. 
D)  13 in.

Question 8

Graph the conic section with focus   and the given directrix and eccentricity. Directrix

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 9

Find the area of the indicated region. One leaf of

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 10

Find the rectangular representation of the given polar point.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 11

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 12

Which graph below corresponds to the given parametric equations?

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 13

Find rectangular coordinates for the given polar point.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 14

Find a polar equation for the conic section with focus   and the given directrix and eccentricity. Directrix

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 15

Find the rectangular representation of the given polar point.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 16

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.) r = 2

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 17

Find the slope of the tangent line to the given curve at the indicated point.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 18

Find the vertices, foci, and directrices of the given hyperbola.

Accepted Answer

A)  vertices (-3, -14), (-3, 4); foci   , directrices   
B)  vertices (-12, -5), (6, -5); foci   , directrices   
C)  vertices (-3, -14), (-3, 4); foci   , directrices   
D)  vertices (-12, -5), (6, -5); foci   , directrices   
A)  vertices (-3, -14), (-3, 4); foci   , directrices   
B)  vertices (-12, -5), (6, -5); foci   , directrices   
C)  vertices (-3, -14), (-3, 4); foci   , directrices   
D)  vertices (-12, -5), (6, -5); foci   , directrices

Question 19

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5].

Accepted Answer

A)  
  
B)  17   
C)    
D)    
A)  
  
B)  17   
C)    
D)

Question 20

Which graph below corresponds to the given parametric equations?

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Find a corresponding x-y equation.

Find the area enclosed by the given curve.

Identify a range of values of that produces one copy of the graph.

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Find all points of intersection of the two curves.

Graph the conic section with focus and the given directrix and eccentricity. Directrix

Find the area of the indicated region. One leaf of

Find the rectangular representation of the given polar point.

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Which graph below corresponds to the given parametric equations?

Find rectangular coordinates for the given polar point.

Find a polar equation for the conic section with focus and the given directrix and eccentricity. Directrix

Find the rectangular representation of the given polar point.

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.) r = 2

Find the slope of the tangent line to the given curve at the indicated point.

Find the vertices, foci, and directrices of the given hyperbola.

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5].

Which graph below corresponds to the given parametric equations?

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Integration Techniques

First-Order Differential Equations

Infinite Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

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Exam 10: Parametric Equations and Polar Coordinates

Find a corresponding x-y equation.

Find the area enclosed by the given curve.

Identify a range of values of that produces one copy of the graph.

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Find all points of intersection of the two curves.

Graph the conic section with focus and the given directrix and eccentricity. Directrix

Find the area of the indicated region. One leaf of

Find the rectangular representation of the given polar point.

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Which graph below corresponds to the given parametric equations?

Find rectangular coordinates for the given polar point.

Find a polar equation for the conic section with focus and the given directrix and eccentricity. Directrix

Find the rectangular representation of the given polar point.

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.) r = 2

Find the slope of the tangent line to the given curve at the indicated point.

Find the vertices, foci, and directrices of the given hyperbola.

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5].

Which graph below corresponds to the given parametric equations?

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Integration Techniques

First-Order Differential Equations

Infinite Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters