Question 1

Use the Quadratic Formula to solve for   . ​   ​

Accepted Answer

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

Question 2

Select the standard form of the equation of the parabola and determine the coordinates of the focus. ​
​   ​

Accepted Answer

A)    ; Focus:   
B)    ; Focus:   
C)    ; Focus:   
D)    Focus:   
E)    ; Focus:   
A)    ; Focus:   
B)    ; Focus:   
C)    ; Focus:   
D)    Focus:   
E)    ; Focus:

Question 3

Find a polar equation of the conic with its focus at the pole. ​
Conics
​Eccentrity
Directrix
Hyperbola     ​

Accepted Answer

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

Question 4

The Falls Incline Railway in Niagara Falls, Ontario, Canada is an inclined railway that was designed to carry people from the City of Niagara Falls to Queen Victoria Park.The railway is approximately 170 feet long with a 40% uphill grade (see figure).Using the origin of a rectangular coordinate system as the base of the inclined plane, find the equation of the line that models the railway track. ​   ​   ​

Accepted Answer

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

Question 5

Select the curve represented by the parametric equations. ​   ​

Accepted Answer

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

Question 6

Select the curve represented by the parametric equations. ​
Curtate cycloid:   ​

Accepted Answer

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

Question 7

Find the vertices and asymptotes of the hyperbola.

Accepted Answer

A) vertices: (0, ±4​) asymptote:   
B) vertices: (±4, 3) asymptote:   
C) vertices: (±4, 0) asymptote:   
D) vertices: (±3, 0) asymptote:   
E) vertices: (0, ±3) asymptote:   
A) vertices: (0, ±4​) asymptote:   
B) vertices: (±4, 3) asymptote:   
C) vertices: (±4, 0) asymptote:   
D) vertices: (±3, 0) asymptote:   
E) vertices: (0, ±3) asymptote:

Question 8

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. ​
Directrix: x = -4
​

Accepted Answer

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

Question 9

A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. ​   ​   ​

Accepted Answer

A) Rectangular coordinates: (0,3) 
B) Rectangular coordinates: (-3,0) 
C) Rectangular coordinates: (3,0) 
D) Rectangular coordinates: (0,-3) 
E) Rectangular coordinates: (3,3) 
A) Rectangular coordinates: (0,3) 
B) Rectangular coordinates: (-3,0) 
C) Rectangular coordinates: (3,0) 
D) Rectangular coordinates: (0,-3) 
E) Rectangular coordinates: (3,3)

Question 10

Select the polar equation of the conic for ​e = 1.0 and identify the conic for the following equation. ​   ​

Accepted Answer

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

Question 11

Select the correct graph of the following equations of the hyperbola and find the center of hyperbola. ​   ​

Accepted Answer

A) Center: (0, 0) ​   
B) Center: (0, 0) ​   
C) Center:   ​   
D) Center: (0, 0) ​   
E) Center:   ​   
A) Center: (0, 0) ​   
B) Center: (0, 0) ​   
C) Center:   ​   
D) Center: (0, 0) ​   
E) Center:   ​

Question 12

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​
Vertices:   ; Foci:   ​

Accepted Answer

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

Question 13

Find a polar equation of the conic with its focus at the pole. ​
Conics
Vertex or vertices
Parabola   ​

Accepted Answer

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

Question 14

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

Accepted Answer

A) Ellipse 
B) Hyperbola 
C) Parabola 
D) Circle 
E) None of the above 
A) Ellipse 
B) Hyperbola 
C) Parabola 
D) Circle 
E) None of the above

Question 15

The Falls Incline Railway in Niagara Falls, Ontario, Canada is an inclined railway that was designed to carry people from the City of Niagara Falls to Queen Victoria Park.The railway is approximately 110 feet long with a 28% uphill grade (see figure).Find the change in elevation from the base to the top of the railway.Round your answers to one decimal place. ​   ​   ​

Accepted Answer

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

Question 16

Identify the conic and select its correct graph. ​   ​

Accepted Answer

A)    Hyperbola ​  
​ 
B)    Hyperbola ​  
​ 
C)    Hyperbola ​  
​
​ 
D)    Hyperbola ​  
​ 
E)    Hyperbola ​  
​ 
A)    Hyperbola ​  
​ 
B)    Hyperbola ​  
​ 
C)    Hyperbola ​  
​
​ 
D)    Hyperbola ​  
​ 
E)    Hyperbola ​  
​

Question 17

Convert the polar equation to rectangular form. ​   ​

Accepted Answer

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

Question 18

By using a graphing utility select the correct graph of the polar equation.Identify the graph. ​   ​

Accepted Answer

A) ​     Hyperbola 
B) ​     Hyperbola 
C) ​     Hyperbola 
D) ​     Hyperbola 
E) ​     Hyperbola 
A) ​     Hyperbola 
B) ​     Hyperbola 
C) ​     Hyperbola 
D) ​     Hyperbola 
E) ​     Hyperbola

Question 19

Select the curve represented by the parametric equations. ​   ​

Accepted Answer

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

Question 20

Select the correct equation of the following graph. ​   ​

Accepted Answer

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

Use the Quadratic Formula to solve for .

Select the standard form of the equation of the parabola and determine the coordinates of the focus.

Find a polar equation of the conic with its focus at the pole. Conics Eccentrity Directrix Hyperbola

Select the curve represented by the parametric equations.

Select the curve represented by the parametric equations. Curtate cycloid:

Find the vertices and asymptotes of the hyperbola.

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Directrix: x = -4

A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates.

Select the polar equation of the conic for e = 1.0 and identify the conic for the following equation.

Select the correct graph of the following equations of the hyperbola and find the center of hyperbola.

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: ; Foci:

Find a polar equation of the conic with its focus at the pole. Conics Vertex or vertices Parabola

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

Identify the conic and select its correct graph.

Convert the polar equation to rectangular form.

By using a graphing utility select the correct graph of the polar equation.Identify the graph.

Select the curve represented by the parametric equations.

Select the correct equation of the following graph.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Exam 6: Topics-In-Analytic-Geometry

Use the Quadratic Formula to solve for . ​ ​

Select the standard form of the equation of the parabola and determine the coordinates of the focus. ​ ​ ​

Find a polar equation of the conic with its focus at the pole. ​ Conics ​Eccentrity Directrix Hyperbola ​

Select the curve represented by the parametric equations. ​ ​

Select the curve represented by the parametric equations. ​ Curtate cycloid: ​

Find the vertices and asymptotes of the hyperbola.

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. ​ Directrix: x = -4 ​

A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. ​ ​ ​

Select the polar equation of the conic for ​e = 1.0 and identify the conic for the following equation. ​ ​

Select the correct graph of the following equations of the hyperbola and find the center of hyperbola. ​ ​

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​ Vertices: ; Foci: ​

Find a polar equation of the conic with its focus at the pole. ​ Conics Vertex or vertices Parabola ​

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

Identify the conic and select its correct graph. ​ ​

Convert the polar equation to rectangular form. ​ ​

By using a graphing utility select the correct graph of the polar equation.Identify the graph. ​ ​

Select the curve represented by the parametric equations. ​ ​

Select the correct equation of the following graph. ​ ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Use the Quadratic Formula to solve for .

Select the standard form of the equation of the parabola and determine the coordinates of the focus.

Find a polar equation of the conic with its focus at the pole. Conics Eccentrity Directrix Hyperbola

Select the curve represented by the parametric equations.

Select the curve represented by the parametric equations. Curtate cycloid:

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Directrix: x = -4

A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates.

Select the polar equation of the conic for e = 1.0 and identify the conic for the following equation.

Select the correct graph of the following equations of the hyperbola and find the center of hyperbola.

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: ; Foci:

Find a polar equation of the conic with its focus at the pole. Conics Vertex or vertices Parabola

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

Identify the conic and select its correct graph.

Convert the polar equation to rectangular form.

By using a graphing utility select the correct graph of the polar equation.Identify the graph.

Select the curve represented by the parametric equations.

Select the correct equation of the following graph.