Question 1

Graph. 
-  +   = 1

Accepted Answer

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

Question 2

Find the area of the specified region.
-Shared by the cardioids r = 4(1 + sin $\theta$) and r = 4(1 - sin $\theta$)

Accepted Answer

A)  4(5$\pi$ + 8) 
B)  8(3$\pi$- 8) 
C)  1616 
D)  8(3$\pi$ + 8) 
A)  4(5$\pi$ + 8) 
B)  8(3$\pi$- 8) 
C)  1616 
D)  8(3$\pi$ + 8)

Question 3

Replace the polar equation with an equivalent Cartesian equation.
-6r cos $\theta$+ 2r sin $\theta$ = 1

Accepted Answer

A)  6x + 2y =   +   
B)    +   = 1 
C)  6y + 2x = 1 
D)  6x + 2y = 1 
A)  6x + 2y =   +   
B)    +   = 1 
C)  6y + 2x = 1 
D)  6x + 2y = 1

Question 4

Find the area of the specified region.
-Inside the smaller loop of the limacon r = 5 + 10 sin $\theta$

Accepted Answer

A)  25$\pi$ 
B)    
C)  5(3   -  $\pi$) 
D)    (2 $\pi$ - 3   ) 
A)  25$\pi$ 
B)    
C)  5(3   -  $\pi$) 
D)    (2 $\pi$ - 3   )

Question 5

Find the area of the specified region.
-Inside the circle r =   sin $\theta$ and outside the cardioid r = 1 + cos $\theta$

Accepted Answer

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

Question 6

Graph the parabola.
-y = -4x2

Accepted Answer

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

Question 7

Solve the problem.  
-Find the foci and asymptotes of the following hyperbola: 16   -   = 16

Accepted Answer

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

Question 8

Graph the pair of parametric equations with the aid of a graphing calculator.
-x = 6t - 6 sin t, y = 6 - 6 cos t, -2$\pi$ $\le$ t $\le$2$\pi$

Accepted Answer

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

Question 9

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 10

Calculate the arc length of the indicated portion of the curve r(t).
-r(t) = 11   i + 2   j + 10   k, 1 $\le$ t $\le$ 2

Accepted Answer

A)  1575 
B)  525 
C)  105 
D)  35 
A)  1575 
B)  525 
C)  105 
D)  35

Question 11

Plot the point whose polar coordinates are given.
-( 2, 9$\pi$/4)

Accepted Answer

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

Question 12

Find the Cartesian coordinates of the given point.
-( -8, 0)

Accepted Answer

A)  ( 8, 0) 
B)  (-8, 0) 
C)  ( 0, -8) 
D)  (0, 8) 
A)  ( 8, 0) 
B)  (-8, 0) 
C)  ( 0, -8) 
D)  (0, 8)

Question 13

Solve the problem.  
-Find the foci and asymptotes of the following hyperbola:   -   = 50

Accepted Answer

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

Question 14

Calculate the arc length of the indicated portion of the curve r(t).
-r(t) =       i + ( 7t sin t)j + ( 7t cos t)k ; -4 $\le$ t$\le$ 5

Accepted Answer

A)  294 
B)  126 
C)  94.5 
D)  150.5 
A)  294 
B)  126 
C)  94.5 
D)  150.5

Question 15

Find the area of the specified region.
-Inside the circle r = -4 sin $\theta$ and outside the circle r = 2

Accepted Answer

A)    (2  $\pi$+ 3   ) 
B)    (4  $\pi$ - 3   ) 
C)     $\pi$ 
D)  2 $\pi$ 
A)    (2  $\pi$+ 3   ) 
B)    (4  $\pi$ - 3   ) 
C)     $\pi$ 
D)  2 $\pi$

Question 16

Find the Cartesian coordinates of the given point.
-

Accepted Answer

A)  ( 4   , -4   ) 
B)  ( 4   , -4) 
C)  ( -4   , -4   ) 
D)  (-8   , -8   ) 
A)  ( 4   , -4   ) 
B)  ( 4   , -4) 
C)  ( -4   , -4   ) 
D)  (-8   , -8   )

Question 17

Replace the polar equation with an equivalent Cartesian equation.
-  = 30r cos $\theta$

Accepted Answer

A)  x = 30 
B)    +   = 225 
C)    +   = 225 
D)    +   = 0 
A)  x = 30 
B)    +   = 225 
C)    +   = 225 
D)    +   = 0

Question 18

Find the Cartesian coordinates of the given point.
-

Accepted Answer

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

Question 19

Replace the polar equation with an equivalent Cartesian equation.
-r =

Accepted Answer

A)    +   = 1 
B)  7y - 8x = 1 
C)  7x - 8y = 1 
D)    = 1 
A)    +   = 1 
B)  7y - 8x = 1 
C)  7x - 8y = 1 
D)    = 1

Question 20

Solve the problem.  
-Find the vertices and foci of the following hyperbola:   -   = 1

Accepted Answer

A)  Vertices: ( 81, 0), (-81, 0); Foci: ( 10, 0), (-10, 0) 
B)  Vertices: (0, 9), (0, -9); Foci: (0, 10), (0, -10) 
C)  Vertices: (9, 0), (-9, 0); Foci: ( 10, 0), (-10, 0) 
D)  Vertices: (0, 10), (0, -10); Foci: (0, 9), (0, -9) 
A)  Vertices: ( 81, 0), (-81, 0); Foci: ( 10, 0), (-10, 0) 
B)  Vertices: (0, 9), (0, -9); Foci: (0, 10), (0, -10) 
C)  Vertices: (9, 0), (-9, 0); Foci: ( 10, 0), (-10, 0) 
D)  Vertices: (0, 10), (0, -10); Foci: (0, 9), (0, -9)

Graph. - + = 1

Find the area of the specified region. -Shared by the cardioids r = 4(1 + sin $\theta$ ) and r = 4(1 - sin $\theta$ )

Replace the polar equation with an equivalent Cartesian equation. -6r cos $\theta$ + 2r sin $\theta$ = 1

Find the area of the specified region. -Inside the smaller loop of the limacon r = 5 + 10 sin $\theta$

Find the area of the specified region. -Inside the circle r = $Find the area of the specified region. -Inside the circle r = sin \theta and outside the cardioid r = 1 + cos \theta$ sin $\theta$ and outside the cardioid r = 1 + cos $\theta$

Graph the parabola. -y = -4x²

Solve the problem. -Find the foci and asymptotes of the following hyperbola: 16 - = 16

Graph the pair of parametric equations with the aid of a graphing calculator. -x = 6t - 6 sin t, y = 6 - 6 cos t, -2 $\pi$ $\le$ t $\le$ 2 $\pi$ $Graph the pair of parametric equations with the aid of a graphing calculator. -x = 6t - 6 sin t, y = 6 - 6 cos t, -2 \pi \le t \le 2 \pi$

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

Plot the point whose polar coordinates are given. -( 2, 9 $\pi$ /4) $Plot the point whose polar coordinates are given. -( 2, 9 \pi /4)$

Find the Cartesian coordinates of the given point. -( -8, 0)

Solve the problem. -Find the foci and asymptotes of the following hyperbola: - = 50

Find the area of the specified region. -Inside the circle r = -4 sin $\theta$ and outside the circle r = 2

Find the Cartesian coordinates of the given point. -

Replace the polar equation with an equivalent Cartesian equation. - $Replace the polar equation with an equivalent Cartesian equation. - = 30r cos \theta$ = 30r cos $\theta$

Find the Cartesian coordinates of the given point. -

Replace the polar equation with an equivalent Cartesian equation. -r =

Solve the problem. -Find the vertices and foci of the following hyperbola: - = 1

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

Graph. - + = 1

Find the area of the specified region. -Shared by the cardioids r = 4(1 + sin θ\thetaθ ) and r = 4(1 - sin θ\thetaθ )

Replace the polar equation with an equivalent Cartesian equation. -6r cos θ\thetaθ + 2r sin θ\thetaθ = 1

Find the area of the specified region. -Inside the smaller loop of the limacon r = 5 + 10 sin θ\thetaθ

Find the area of the specified region. -Inside the circle r = sin θ\thetaθ and outside the cardioid r = 1 + cos θ\thetaθ

Graph the parabola. -y = -4x2

Solve the problem. -Find the foci and asymptotes of the following hyperbola: 16 - = 16

Graph the pair of parametric equations with the aid of a graphing calculator. -x = 6t - 6 sin t, y = 6 - 6 cos t, -2 π\piπ ≤\le≤ t ≤\le≤ 2 π\piπ

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

Calculate the arc length of the indicated portion of the curve r(t). -r(t) = 11 i + 2 j + 10 k, 1 ≤\le≤ t ≤\le≤ 2

Plot the point whose polar coordinates are given. -( 2, 9 π\piπ /4)

Find the Cartesian coordinates of the given point. -( -8, 0)

Solve the problem. -Find the foci and asymptotes of the following hyperbola: - = 50

Calculate the arc length of the indicated portion of the curve r(t). -r(t) = i + ( 7t sin t)j + ( 7t cos t)k ; -4 ≤\le≤ t ≤\le≤ 5

Find the area of the specified region. -Inside the circle r = -4 sin θ\thetaθ and outside the circle r = 2

Find the Cartesian coordinates of the given point. -

Replace the polar equation with an equivalent Cartesian equation. - = 30r cos θ\thetaθ

Find the Cartesian coordinates of the given point. -

Replace the polar equation with an equivalent Cartesian equation. -r =

Solve the problem. -Find the vertices and foci of the following hyperbola: - = 1

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

Find the area of the specified region. -Shared by the cardioids r = 4(1 + sin $\theta$ ) and r = 4(1 - sin $\theta$ )

Replace the polar equation with an equivalent Cartesian equation. -6r cos $\theta$ + 2r sin $\theta$ = 1

Find the area of the specified region. -Inside the smaller loop of the limacon r = 5 + 10 sin $\theta$

Find the area of the specified region. -Inside the circle r = $Find the area of the specified region. -Inside the circle r = sin \theta and outside the cardioid r = 1 + cos \theta$ sin $\theta$ and outside the cardioid r = 1 + cos $\theta$

Graph the parabola. -y = -4x²

Graph the pair of parametric equations with the aid of a graphing calculator. -x = 6t - 6 sin t, y = 6 - 6 cos t, -2 $\pi$ $\le$ t $\le$ 2 $\pi$ $Graph the pair of parametric equations with the aid of a graphing calculator. -x = 6t - 6 sin t, y = 6 - 6 cos t, -2 \pi \le t \le 2 \pi$

Plot the point whose polar coordinates are given. -( 2, 9 $\pi$ /4) $Plot the point whose polar coordinates are given. -( 2, 9 \pi /4)$

Find the area of the specified region. -Inside the circle r = -4 sin $\theta$ and outside the circle r = 2

Replace the polar equation with an equivalent Cartesian equation. - $Replace the polar equation with an equivalent Cartesian equation. - = 30r cos \theta$ = 30r cos $\theta$