Question 1

Convert the polar equation   to rectangular form.

Accepted Answer

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

Question 2

Find the eccentricity of the ellipse given by   .

Accepted Answer

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

Question 3

Uranus moves in an elliptical orbit with the sun at one of the foci. The length of the half of the major axis is 2,876,769,540 kilometers, and the eccentricity is 0.0444. Find the minimum distance (perihelion) of Uranus from the sun. Round your answer to nearest kilometer. ​

Accepted Answer

A)  3,004,498,108 km 
B)  2,749,040,972 km 
C)  2,819,234,149 km 
D)  7,819,870,365 km 
E)  2,934,304,931 km 
A)  3,004,498,108 km 
B)  2,749,040,972 km 
C)  2,819,234,149 km 
D)  7,819,870,365 km 
E)  2,934,304,931 km B

Question 4

Find the focus of the parabola given by   . ​

Accepted Answer

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

Question 5

Neptune moves in an elliptical orbit with the sun at one of the foci. The length of half of the major axis is   kilometers, and the eccentricity is 0.0086. Find the perihelion distance of Neptune from the sun. Round your answer to the nearest kilometers.

Accepted Answer

A)  4,536,682,800 kilometers 
B)  4,459,317,201 kilometers 
C)  4,459,317,200 kilometers 
D)  8,918,634,399 kilometers 
E)  8,918,634,401 kilometers 
A)  4,536,682,800 kilometers 
B)  4,459,317,201 kilometers 
C)  4,459,317,200 kilometers 
D)  8,918,634,399 kilometers 
E)  8,918,634,401 kilometers

Question 6

Find the eccentricity of the polar equation   .

Accepted Answer

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

Question 7

Write an integral that represents the area of the shaded region for   as shown in the figure. Do not evaluate the integral. ​   ​

Accepted Answer

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

Question 8

Match the graph with its polar equation. ​   ​

Accepted Answer

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

Question 9

Find all points (if any) of horizontal and vertical tangency to the curve   .

Accepted Answer

A)  horizontal tangents:   , vertical tangent: none 
B)  horizontal tangent: none, vertical tangents:   
C)  horizontal tangents:   , vertical tangent: none 
D)  horizontal tangent: none, vertical tangents:   
E)  horizontal tangent: none, vertical tangent: none 
A)  horizontal tangents:   , vertical tangent: none 
B)  horizontal tangent: none, vertical tangents:   
C)  horizontal tangents:   , vertical tangent: none 
D)  horizontal tangent: none, vertical tangents:   
E)  horizontal tangent: none, vertical tangent: none

Question 10

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

Accepted Answer

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

Question 11

Find an equation of the hyperbola with vertices   and asymptotes   .

Accepted Answer

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

Question 12

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

Accepted Answer

A)  parabola 
B)  ellipse 
C)  circle 
D)  hyperbola 
A)  parabola 
B)  ellipse 
C)  circle 
D)  hyperbola

Question 13

Match the graph with its polar equation. ​   ​

Accepted Answer

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

Question 14

Find the arc length of the curve   on the interval   . Round your answer to three decimal places.

Accepted Answer

A)  287.453 
B)  191.635 
C)  193.606 
D)  66.480 
E)  99.721 
A)  287.453 
B)  191.635 
C)  193.606 
D)  66.480 
E)  99.721

Question 15

Use the result, "the set of parametric equations for the circle is   " to find a set of parametric equations for the circle with a center   and radius   .

Accepted Answer

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

Question 16

Identify any points at which the Folium of Descartes   is not smooth. Round your answer to two decimal places, if necessary.

Accepted Answer

A)  not smooth when   
B)  not smooth when   
C)  not smooth when   
D)  smooth everywhere 
E)  not smooth when   
A)  not smooth when   
B)  not smooth when   
C)  not smooth when   
D)  smooth everywhere 
E)  not smooth when

Question 17

Find an equation of the hyperbola with vertices   and asymptotes   .

Accepted Answer

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

Question 18

Find   and   if possible, and find the slope and concavity (if possible) at the point corresponding to t = 2.

Accepted Answer

A)    : slope   and concave up 
B)    slope 8 and concave down 
C)    slope 16 and concave up 
D)    : slope -8 and concave down 
E)    : slope   and concave up 
A)    : slope   and concave up 
B)    slope 8 and concave down 
C)    slope 16 and concave up 
D)    : slope -8 and concave down 
E)    : slope   and concave up

Question 19

Find the length of the curve over the given interval.

Accepted Answer

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

Question 20

Determine the t intervals on which the curve   is concave downward or concave upward.

Accepted Answer

A)  concave downward:   ; concave upward:   
B)  concave downward:   ; concave upward:   
C)  concave downward:   
D)  concave upward:   
E)  concave downward:   
A)  concave downward:   ; concave upward:   
B)  concave downward:   ; concave upward:   
C)  concave downward:   
D)  concave upward:   
E)  concave downward:

Convert the polar equation to rectangular form.

Find the eccentricity of the ellipse given by .

Uranus moves in an elliptical orbit with the sun at one of the foci. The length of the half of the major axis is 2,876,769,540 kilometers, and the eccentricity is 0.0444. Find the minimum distance (perihelion) of Uranus from the sun. Round your answer to nearest kilometer.

Find the focus of the parabola given by .

Neptune moves in an elliptical orbit with the sun at one of the foci. The length of half of the major axis is kilometers, and the eccentricity is 0.0086. Find the perihelion distance of Neptune from the sun. Round your answer to the nearest kilometers.

Find the eccentricity of the polar equation .

Write an integral that represents the area of the shaded region for as shown in the figure. Do not evaluate the integral.

Match the graph with its polar equation.

Find all points (if any) of horizontal and vertical tangency to the curve .

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

Find an equation of the hyperbola with vertices and asymptotes .

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

Match the graph with its polar equation.

Find the arc length of the curve on the interval . Round your answer to three decimal places.

Use the result, "the set of parametric equations for the circle is " to find a set of parametric equations for the circle with a center and radius .

Identify any points at which the Folium of Descartes is not smooth. Round your answer to two decimal places, if necessary.

Find an equation of the hyperbola with vertices and asymptotes .

Find and if possible, and find the slope and concavity (if possible) at the point corresponding to t = 2.

Find the length of the curve over the given interval.

Determine the t intervals on which the curve is concave downward or concave upward.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 10: Conics, Parametric Equations, and Polar Coordinates

Convert the polar equation to rectangular form.

Find the eccentricity of the ellipse given by .

Uranus moves in an elliptical orbit with the sun at one of the foci. The length of the half of the major axis is 2,876,769,540 kilometers, and the eccentricity is 0.0444. Find the minimum distance (perihelion) of Uranus from the sun. Round your answer to nearest kilometer. ​

Find the focus of the parabola given by . ​

Neptune moves in an elliptical orbit with the sun at one of the foci. The length of half of the major axis is kilometers, and the eccentricity is 0.0086. Find the perihelion distance of Neptune from the sun. Round your answer to the nearest kilometers.

Find the eccentricity of the polar equation .

Write an integral that represents the area of the shaded region for as shown in the figure. Do not evaluate the integral. ​ ​

Match the graph with its polar equation. ​ ​

Find all points (if any) of horizontal and vertical tangency to the curve .

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

Find an equation of the hyperbola with vertices and asymptotes .

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

Match the graph with its polar equation. ​ ​

Find the arc length of the curve on the interval . Round your answer to three decimal places.

Use the result, "the set of parametric equations for the circle is " to find a set of parametric equations for the circle with a center and radius .

Identify any points at which the Folium of Descartes is not smooth. Round your answer to two decimal places, if necessary.

Find an equation of the hyperbola with vertices and asymptotes .

Find and if possible, and find the slope and concavity (if possible) at the point corresponding to t = 2.

Find the length of the curve over the given interval.

Determine the t intervals on which the curve is concave downward or concave upward.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Uranus moves in an elliptical orbit with the sun at one of the foci. The length of the half of the major axis is 2,876,769,540 kilometers, and the eccentricity is 0.0444. Find the minimum distance (perihelion) of Uranus from the sun. Round your answer to nearest kilometer.

Find the focus of the parabola given by .

Write an integral that represents the area of the shaded region for as shown in the figure. Do not evaluate the integral.

Match the graph with its polar equation.

Match the graph with its polar equation.