Question 1

Match the equation with its graph.

Accepted Answer

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

Question 2

Match the equation with its graph.

Accepted Answer

A)    
B)    
C)    
D)    
E)  none of these 
A)    
B)    
C)    
D)    
E)  none of these E

Question 3

Match the equation with its graph.

Accepted Answer

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

Question 4

Match the equation with its graph.

Accepted Answer

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

Question 5

Suppose a cable of a suspension bridge is suspended (in the shape of a parabola) between two towers that are 240 meters apart and 40 meters above the roadway as shown in the figure given below. The cable touches the roadway midway between the towers. Find the length of the parabolic supporting cable. Round your answer to two decimal places.

Accepted Answer

A)  280.79 meters 
B)  327.58 meters 
C)  291.18 meters 
D)  245.71 meters 
E)  256.75 meters 
A)  280.79 meters 
B)  327.58 meters 
C)  291.18 meters 
D)  245.71 meters 
E)  256.75 meters

Question 6

Find an equation of the ellipse with vertices   and eccentricity   .

Accepted Answer

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

Question 7

Find an equation of the parabola with vertex   and directrix   .

Accepted Answer

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

Question 8

Find the vertex of the parabola given by   .

Accepted Answer

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

Question 9

Find an equation of the hyperbola with vertices   and asymptotes   .

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

Find the eccentricity of the ellipse given by   .

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

Find the directrix of the parabola given by   .

Accepted Answer

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

Question 14

Find an equation of the hyperbola with vertices   and asymptotes   .

Accepted Answer

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

Question 15

Suppose a church window is bounded above by a parabola and below by the arc of a circle as shown in figure given below. Find the surface area of the window. Round your answer to three decimal places.

Accepted Answer

A)  147.477 ft2 
B)  62.143 ft2 
C)  81.292 ft2 
D)  53.610 ft2 
E)  184.590 ft2 
A)  147.477 ft2 
B)  62.143 ft2 
C)  81.292 ft2 
D)  53.610 ft2 
E)  184.590 ft2

Question 16

Find the vertex, focus, and directrix of the parabola and sketch its graph.

Accepted Answer

A)  vertex:   ; focus:   ; directrix x = -1   
B)  vertex:   ; focus:   ; directrix x = 1   
C)  vertex:   ; focus:   ; directrix x = 3   
D)  vertex:   ; focus:   ; directrix x = 3   
E)  vertex:   ; focus:   ; directrix x = -1   
A)  vertex:   ; focus:   ; directrix x = -1   
B)  vertex:   ; focus:   ; directrix x = 1   
C)  vertex:   ; focus:   ; directrix x = 3   
D)  vertex:   ; focus:   ; directrix x = 3   
E)  vertex:   ; focus:   ; directrix x = -1

Question 17

Earth moves in an elliptical orbit with the sun at one of the foci. The length of the half of the major axis is 149,598,000 kilometers, and the eccentricity is 0.0167. Find the maximum distance (aphelion) of Earth from the sun. Round your answer to nearest kilometer.

Accepted Answer

A)  146,606,040 km 
B)  2,498,287 km 
C)  152,589,960 km 
D)  152,096,287 km 
E)  147,099,713 km 
A)  146,606,040 km 
B)  2,498,287 km 
C)  152,589,960 km 
D)  152,096,287 km 
E)  147,099,713 km

Question 18

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

Accepted Answer

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

Question 19

Find the vertices of the ellipse given by   .

Accepted Answer

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

Question 20

Saturn moves in an elliptical orbit with the sun at one of the foci. The length of the half of the major axis is 1,433,448,036 kilometers, and the eccentricity is 0.0557. Find the minimum distance (perihelion) of Saturn from the sun. Round your answer to nearest kilometer.

Accepted Answer

A)  1,462,116,997 km 
B)  1,353,604,980 km 
C)  1,404,779,075 km 
D)  1,513,291,092 km 
E)  79,843,056 km 
A)  1,462,116,997 km 
B)  1,353,604,980 km 
C)  1,404,779,075 km 
D)  1,513,291,092 km 
E)  79,843,056 km

Exam 10: Section 1: Conics, Parametric Equations, and Polar Coordinates

Match the equation with its graph.

Match the equation with its graph.

Match the equation with its graph.

Match the equation with its graph.

Find an equation of the ellipse with vertices and eccentricity .

Find an equation of the parabola with vertex and directrix .

Find the vertex of the parabola given by .

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.

Find the eccentricity of the ellipse given by .

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

Find the directrix of the parabola given by .

Find an equation of the hyperbola with vertices and asymptotes .

Suppose a church window is bounded above by a parabola and below by the arc of a circle as shown in figure given below. Find the surface area of the window. Round your answer to three decimal places.

Find the vertex, focus, and directrix of the parabola and sketch its graph.

Earth moves in an elliptical orbit with the sun at one of the foci. The length of the half of the major axis is 149,598,000 kilometers, and the eccentricity is 0.0167. Find the maximum distance (aphelion) of Earth from the sun. Round your answer to nearest kilometer.

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

Find the vertices of the ellipse given by .

Saturn moves in an elliptical orbit with the sun at one of the foci. The length of the half of the major axis is 1,433,448,036 kilometers, and the eccentricity is 0.0557. Find the minimum distance (perihelion) of Saturn from the sun. Round your answer to nearest kilometer.

Section 1: Preparation for Calculus

Section 2: Preparation for Calculus

Section 3: Preparation for Calculus

Section 4: Preparation for Calculus

Section 5: Preparation for Calculus

Section 6: Preparation for Calculus

Section 1: Limits and Their Properties

Section 2: Limits and Their Properties

Section 3: Limits and Their Properties

Section 4: Limits and Their Properties

Section 5 : Limits and Their Properties

Section 1 : Differentiation

Section 2: Differentiation

Section 3: Differentiation

Section 4 : Differentiation

Section 5: Differentiation

Section 6: Differentiation

Section 7: Differentiation

Section 8: Differentiation

Section 1 : Applications of Differentiation

Section 2: Applications of Differentiation

Section 3: Applications of Differentiation

Section 4: Applications of Differentiation

Section 5: Applications of Differentiation

Section 6: Applications of Differentiation

Section 7: Applications of Differentiation

Section 8: Applications of Differentiation

Section 1: Integration

Section 2: Integration

Section 3: Integration

Section 4: Integration

Section 5: Integration

Section 6: Integration

Section 7: Integration

Section 8: Integration

Section 9: Integration

Section 1: Differential Equations

Section 2: Differential Equations

Section 3: Differential Equations

Section 4: Differential Equations

Section 5: Differential Equations

Section 1: Applications of Integration

Section 2: Applications of Integration

Section 3: Applications of Integration

Section 4: Applications of Integration

Section 5: Applications of Integration

Section 6: Applications of Integration

Section 7: Applications of Integration

Section 1: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 2: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 3: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 4: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 5: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 6: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 7: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 8: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 1: Infinite Series

Section 2: Infinite Series

Section 3: Infinite Series

Section 4: Infinite Series