Question 1

Determine if the given polar coordinates represent the same point.
-( 2, $\pi$/2), (-2, 3$\pi$/2)

Accepted Answer

A) True 
 B)False

Question 2

Plot the point whose polar coordinates are given.
-( -4, 0)

Accepted Answer

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

Question 3

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions.
-Vertices at (0, 6) and (0, -6); foci at (0, 11) and (0, -11)

Accepted Answer

A)    -   = 1 
B)    -   = 1 
C)    -   = 1 
D)    -   = 1 
A)    -   = 1 
B)    -   = 1 
C)    -   = 1 
D)    -   = 1

Question 4

Graph the parabola or ellipse. Include the directrix that corresponds to the focus at the origin.
-r =

Accepted Answer

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

Question 5

Find the area of the specified region.
-Inside the lemniscate   = 6 sin 2$\theta$ and outside the circle r =

Accepted Answer

A)  3   - $\pi$ 
B)    (2 $\pi$ + 3   ) 
C)  2$\pi$ 
D)  3   - $\pi$ + 6 
A)  3   - $\pi$ 
B)    (2 $\pi$ + 3   ) 
C)  2$\pi$ 
D)  3   - $\pi$ + 6

Question 6

Choose the equation that matches the graph.
-

Accepted Answer

A)    = 4x 
B)    = -4y 
C)    = -4x 
D)  -4   = x 
A)    = 4x 
B)    = -4y 
C)    = -4x 
D)  -4   = x

Question 7

Graph. 
-36   + 12   = 192

Accepted Answer

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

Question 8

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions.
-Vertices at ( 4, 0) and ( -4, 0); foci at ( 9, 0) and ( -9, 0)

Accepted Answer

A)    -   = 1 
B)    -   = 1 
C)    -   = 1 
D)    -   = 1 
A)    -   = 1 
B)    -   = 1 
C)    -   = 1 
D)    -   = 1

Question 9

Find the focus and directrix of the parabola.
-  = 8x

Accepted Answer

A)  ( 2, 0); x = 2 
B)  (0, 2); y = -2 
C)  ( 2, 0); x = -2 
D)  ( 2, 2); x = 2 
A)  ( 2, 0); x = 2 
B)  (0, 2); y = -2 
C)  ( 2, 0); x = -2 
D)  ( 2, 2); x = 2

Question 10

Graph the polar equation.
-r = 4(1 -sin $\theta$)

Accepted Answer

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

Question 11

Graph the polar equation.
-r = 4 cos 8$\theta$

Accepted Answer

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

Question 12

Find the area of the specified region.
-Inside the limacon r = 9 + 6 sin $\theta$

Accepted Answer

A)  99$\pi$ 
B)  198$\pi$- 108 
C)  99$\pi$+ 108 
D)  198$\pi$ 
A)  99$\pi$ 
B)  198$\pi$- 108 
C)  99$\pi$+ 108 
D)  198$\pi$

Question 13

Find an equation of the following curve.
-A hyperbola centered at the origin having vertex at (0, -3) and eccentricity equal to 2

Accepted Answer

A)    -   = 1 
B)    -   = 1 
C)    -   = 1 
D)    +   = 1 
A)    -   = 1 
B)    -   = 1 
C)    -   = 1 
D)    +   = 1

Question 14

Find the area of the specified region.
-Inside one loop of the lemniscate   = 6 cos 2$\theta$

Accepted Answer

A)  6 
B)    
C)  12 
D)  3 
A)  6 
B)    
C)  12 
D)  3

Question 15

Find the focus and directrix of the parabola.
-  = 32y

Accepted Answer

A)  (0, -8); x = - 8 
B) ( 8, 0); x = 8 
C)  (0, 8); y = -8 
D)  ( 8, 0); y = 8 
A)  (0, -8); x = - 8 
B) ( 8, 0); x = 8 
C)  (0, 8); y = -8 
D)  ( 8, 0); y = 8

Question 16

Determine if the given polar coordinates represent the same point.
-( 10, $\pi$/6), ( 10, 7$\pi$/6)

Accepted Answer

A) True 
 B)False

Question 17

Determine if the given polar coordinates represent the same point.
-( 8, $\pi$/6), (-8, 7$\pi$/6)

Accepted Answer

A) True 
 B)False

Question 18

Choose the equation that matches the graph.   
-

Accepted Answer

A)    -   = 1 
B)    -   = 1 
C)    -   = 1 
D)    +   = 1 
A)    -   = 1 
B)    -   = 1 
C)    -   = 1 
D)    +   = 1

Question 19

Find the area of the specified region.
-Inside the graph of r = 3 + cos 3$\theta$

Accepted Answer

A)    
B)  19 $\pi$ 
C)    +   
D)  19 $\pi$ +   
A)    
B)  19 $\pi$ 
C)    +   
D)  19 $\pi$ +

Question 20

Choose the equation that matches the graph.   
-

Accepted Answer

A)    -   = 1 
B)    -   = 1 
C)    -   = 1 
D)    +   = 1 
A)    -   = 1 
B)    -   = 1 
C)    -   = 1 
D)    +   = 1

Determine if the given polar coordinates represent the same point. -( 2, $\pi$ /2), (-2, 3 $\pi$ /2)

Plot the point whose polar coordinates are given. -( -4, 0)

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions. -Vertices at (0, 6) and (0, -6); foci at (0, 11) and (0, -11)

Graph the parabola or ellipse. Include the directrix that corresponds to the focus at the origin. -r =

Choose the equation that matches the graph. -

Graph. -36 + 12 = 192

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions. -Vertices at ( 4, 0) and ( -4, 0); foci at ( 9, 0) and ( -9, 0)

Find the focus and directrix of the parabola. - = 8x

Graph the polar equation. -r = 4(1 -sin $\theta$ ) $Graph the polar equation. -r = 4(1 -sin \theta )$

Graph the polar equation. -r = 4 cos 8 $\theta$ $Graph the polar equation. -r = 4 cos 8 \theta$

Find the area of the specified region. -Inside the limacon r = 9 + 6 sin $\theta$

Find an equation of the following curve. -A hyperbola centered at the origin having vertex at (0, -3) and eccentricity equal to 2

Find the area of the specified region. -Inside one loop of the lemniscate $Find the area of the specified region. -Inside one loop of the lemniscate = 6 cos 2 \theta$ = 6 cos 2 $\theta$

Find the focus and directrix of the parabola. - = 32y

Determine if the given polar coordinates represent the same point. -( 10, $\pi$ /6), ( 10, 7 $\pi$ /6)

Determine if the given polar coordinates represent the same point. -( 8, $\pi$ /6), (-8, 7 $\pi$ /6)

Choose the equation that matches the graph. -

Find the area of the specified region. -Inside the graph of r = 3 + cos 3 $\theta$

Choose the equation that matches the graph. -

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Exam 12: Parametric and Polar Curves

Determine if the given polar coordinates represent the same point. -( 2, π\piπ /2), (-2, 3 π\piπ /2)

Plot the point whose polar coordinates are given. -( -4, 0)

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions. -Vertices at (0, 6) and (0, -6); foci at (0, 11) and (0, -11)

Graph the parabola or ellipse. Include the directrix that corresponds to the focus at the origin. -r =

Find the area of the specified region. -Inside the lemniscate = 6 sin 2 θ\thetaθ and outside the circle r =

Choose the equation that matches the graph. -

Graph. -36 + 12 = 192

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions. -Vertices at ( 4, 0) and ( -4, 0); foci at ( 9, 0) and ( -9, 0)

Find the focus and directrix of the parabola. - = 8x

Graph the polar equation. -r = 4(1 -sin θ\thetaθ )

Graph the polar equation. -r = 4 cos 8 θ\thetaθ

Find the area of the specified region. -Inside the limacon r = 9 + 6 sin θ\thetaθ

Find an equation of the following curve. -A hyperbola centered at the origin having vertex at (0, -3) and eccentricity equal to 2

Find the area of the specified region. -Inside one loop of the lemniscate = 6 cos 2 θ\thetaθ

Find the focus and directrix of the parabola. - = 32y

Determine if the given polar coordinates represent the same point. -( 10, π\piπ /6), ( 10, 7 π\piπ /6)

Determine if the given polar coordinates represent the same point. -( 8, π\piπ /6), (-8, 7 π\piπ /6)

Choose the equation that matches the graph. -

Find the area of the specified region. -Inside the graph of r = 3 + cos 3 θ\thetaθ

Choose the equation that matches the graph. -

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Determine if the given polar coordinates represent the same point. -( 2, $\pi$ /2), (-2, 3 $\pi$ /2)

Graph the polar equation. -r = 4(1 -sin $\theta$ ) $Graph the polar equation. -r = 4(1 -sin \theta )$

Graph the polar equation. -r = 4 cos 8 $\theta$ $Graph the polar equation. -r = 4 cos 8 \theta$

Find the area of the specified region. -Inside the limacon r = 9 + 6 sin $\theta$

Find the area of the specified region. -Inside one loop of the lemniscate $Find the area of the specified region. -Inside one loop of the lemniscate = 6 cos 2 \theta$ = 6 cos 2 $\theta$

Determine if the given polar coordinates represent the same point. -( 10, $\pi$ /6), ( 10, 7 $\pi$ /6)

Determine if the given polar coordinates represent the same point. -( 8, $\pi$ /6), (-8, 7 $\pi$ /6)

Find the area of the specified region. -Inside the graph of r = 3 + cos 3 $\theta$