Question 1

Choose the equation that matches the graph.
-

Accepted Answer

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

Question 2

Graph the polar equation.
-r = 3( 1 + 2 sin $\theta$)

Accepted Answer

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

Question 3

Find the Cartesian coordinates of the given point.
-

Accepted Answer

A)  ( 5   , 5) 
B) ( 10   , 10   ) 
C)  ( 5   , 5   ) 
D)  ( 10, 10) 
A)  ( 5   , 5) 
B) ( 10   , 10   ) 
C)  ( 5   , 5   ) 
D)  ( 10, 10)

Question 4

Determine if the given polar coordinates represent the same point.
-( 10, $\pi$/4), ( 10, 5$\pi$/4)

Accepted Answer

A) True 
 B)False

Question 5

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

Accepted Answer

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

Question 6

Find the length of the curve.
-The line segment r = 5 sec $\theta$, 0 $\le$ $\theta$$\le$

Accepted Answer

A)  5 ln   
B)    (   + ln(   + 1)) 
C)  5 
D)    
A)  5 ln   
B)    (   + ln(   + 1)) 
C)  5 
D)

Question 7

Find the Cartesian coordinates of the given point.
-

Accepted Answer

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

Question 8

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions.
-Asymptotes y =   x, y = -   x; one vertex is (0, 18)

Accepted Answer

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

Question 9

Find the area of the specified region.
-Inside the lemniscate   =   sin 2$\theta$, a > 0

Accepted Answer

A)  0 
B)    
C)   $\pi$   
D)    
A)  0 
B)    
C)   $\pi$   
D)

Question 10

Parametric equations and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the
particle and the direction of motion.
-x = 36   , y = 6t, - $\infty$ $\le$ t $\le$ $\infty$

Accepted Answer

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

Question 11

Find the focus and directrix of the parabola.
-x = 10

Accepted Answer

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

Question 12

Choose the equation that matches the graph.   
-

Accepted Answer

A)  4x2 - 25y2 = 100 
B)  25x2 - 4y2 = 100 
C)  25x2 + 4y2 = 100 
D)  4y2 - 25x2 = 100 
A)  4x2 - 25y2 = 100 
B)  25x2 - 4y2 = 100 
C)  25x2 + 4y2 = 100 
D)  4y2 - 25x2 = 100

Question 13

Replace the polar equation with an equivalent Cartesian equation.
-r = -12 csc$\theta$

Accepted Answer

A)  -12x = 1 
B)  y = -12 
C)  x= -12 
D)  -12y = 1 
A)  -12x = 1 
B)  y = -12 
C)  x= -12 
D)  -12y = 1

Question 14

Replace the polar equation with an equivalent Cartesian equation.
-  = 46r cos $\theta$- 6r sin$\theta$- 9

Accepted Answer

A)  46x - 6y = 9 
B)    +   = 9 
C)    +   = 9 
D)    +   = 529 
A)  46x - 6y = 9 
B)    +   = 9 
C)    +   = 9 
D)    +   = 529

Question 15

Calculate the arc length of the indicated portion of the curve r(t).
-r(t) = ( 7 + 2 $ t^{2} $ )i + (2 $ t^{2} $ - 3)j + ( 10 - $ t^{2} $ )k, 1 $\le$ t $\le$ 4

Accepted Answer

A)  51 
B)  135 
C)  153 
D)  45 
A)  51 
B)  135 
C)  153 
D)  45

Question 16

Find the Cartesian coordinates of the given point.
-(   , $\pi$/6)

Accepted Answer

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

Question 17

Solve the problem.  
-Find the foci and asymptotes of the following hyperbola: 4   -   = 4

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Graph the polar equation.
-r = 2 + cos $\theta$

Accepted Answer

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

Question 20

Parametric equations and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the
particle and the direction of motion.
-x = 3t + 4, y = 9t + 3, -$\infty$ $\le$ t $\le$ $\infty$

Accepted Answer

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

Choose the equation that matches the graph. -

Graph the polar equation. -r = 3( 1 + 2 sin $\theta$ ) $Graph the polar equation. -r = 3( 1 + 2 sin \theta )$

Find the Cartesian coordinates of the given point. -

Determine if the given polar coordinates represent the same point. -( 10, $\pi$ /4), ( 10, 5 $\pi$ /4)

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

Find the length of the curve. -The line segment r = 5 sec $\theta$ , 0 $\le$ $\theta$ $\le$ $Find the length of the curve. -The line segment r = 5 sec \theta , 0 \le \theta\le$

Find the Cartesian coordinates of the given point. -

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions. -Asymptotes y = x, y = - x; one vertex is (0, 18)

Find the area of the specified region. -Inside the lemniscate $Find the area of the specified region. -Inside the lemniscate = sin 2 \theta , a > 0$ = $Find the area of the specified region. -Inside the lemniscate = sin 2 \theta , a > 0$ sin 2 $\theta$ , a > 0

Find the focus and directrix of the parabola. -x = 10

Choose the equation that matches the graph. -

Replace the polar equation with an equivalent Cartesian equation. -r = -12 csc $\theta$

Replace the polar equation with an equivalent Cartesian equation. - $Replace the polar equation with an equivalent Cartesian equation. - = 46r cos \theta - 6r sin \theta - 9$ = 46r cos $\theta$ - 6r sin $\theta$ - 9

Calculate the arc length of the indicated portion of the curve r(t). -r(t) = ( 7 + 2 $t^{2}$ )i + (2 $t^{2}$ - 3)j + ( 10 - $t^{2}$ )k, 1 $\le$ t $\le$ 4

Find the Cartesian coordinates of the given point. -( $Find the Cartesian coordinates of the given point. -( , \pi /6)$ , $\pi$ /6)

Solve the problem. -Find the foci and asymptotes of the following hyperbola: 4 - = 4

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

Graph the polar equation. -r = 2 + cos $\theta$ $Graph the polar equation. -r = 2 + cos \theta$

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

Choose the equation that matches the graph. -

Graph the polar equation. -r = 3( 1 + 2 sin θ\thetaθ )

Find the Cartesian coordinates of the given point. -

Determine if the given polar coordinates represent the same point. -( 10, π\piπ /4), ( 10, 5 π\piπ /4)

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

Find the length of the curve. -The line segment r = 5 sec θ\thetaθ , 0 ≤\le≤ θ\thetaθ≤\le≤

Find the Cartesian coordinates of the given point. -

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions. -Asymptotes y = x, y = - x; one vertex is (0, 18)

Find the area of the specified region. -Inside the lemniscate = sin 2 θ\thetaθ , a > 0

Find the focus and directrix of the parabola. -x = 10

Choose the equation that matches the graph. -

Replace the polar equation with an equivalent Cartesian equation. -r = -12 csc θ\thetaθ

Replace the polar equation with an equivalent Cartesian equation. - = 46r cos θ\thetaθ - 6r sin θ\thetaθ - 9

Calculate the arc length of the indicated portion of the curve r(t). -r(t) = ( 7 + 2 t2 t^{2} t2 )i + (2 t2 t^{2} t2 - 3)j + ( 10 - t2 t^{2} t2 )k, 1 ≤\le≤ t ≤\le≤ 4

Find the Cartesian coordinates of the given point. -( , π\piπ /6)

Solve the problem. -Find the foci and asymptotes of the following hyperbola: 4 - = 4

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

Graph the polar equation. -r = 2 + cos θ\thetaθ

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

Graph the polar equation. -r = 3( 1 + 2 sin $\theta$ ) $Graph the polar equation. -r = 3( 1 + 2 sin \theta )$

Determine if the given polar coordinates represent the same point. -( 10, $\pi$ /4), ( 10, 5 $\pi$ /4)

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

Find the length of the curve. -The line segment r = 5 sec $\theta$ , 0 $\le$ $\theta$ $\le$ $Find the length of the curve. -The line segment r = 5 sec \theta , 0 \le \theta\le$

Find the area of the specified region. -Inside the lemniscate $Find the area of the specified region. -Inside the lemniscate = sin 2 \theta , a > 0$ = $Find the area of the specified region. -Inside the lemniscate = sin 2 \theta , a > 0$ sin 2 $\theta$ , a > 0

Replace the polar equation with an equivalent Cartesian equation. -r = -12 csc $\theta$

Replace the polar equation with an equivalent Cartesian equation. - $Replace the polar equation with an equivalent Cartesian equation. - = 46r cos \theta - 6r sin \theta - 9$ = 46r cos $\theta$ - 6r sin $\theta$ - 9

Calculate the arc length of the indicated portion of the curve r(t). -r(t) = ( 7 + 2 $t^{2}$ )i + (2 $t^{2}$ - 3)j + ( 10 - $t^{2}$ )k, 1 $\le$ t $\le$ 4

Find the Cartesian coordinates of the given point. -( $Find the Cartesian coordinates of the given point. -( , \pi /6)$ , $\pi$ /6)

Graph the polar equation. -r = 2 + cos $\theta$ $Graph the polar equation. -r = 2 + cos \theta$