Question 1

Using the graph of the ellipse, determine the coordinates of the foci, vertices, and center.
-

Accepted Answer

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

Question 2

Find the coordinates of the vertex of the parabola.
-

Accepted Answer

A)  (4, 3) 
B)  (0, 4) 
C)  (3, 4) 
D)  (3, 0) 
A)  (4, 3) 
B)  (0, 4) 
C)  (3, 4) 
D)  (3, 0)

Question 3

Find the focus and the directrix of the parabola.
-

Accepted Answer

A)  (5, -2); y = 0 
B)  (5, 0); y = -2 
C)    
D)  (5, -5); y = -3 
A)  (5, -2); y = 0 
B)  (5, 0); y = -2 
C)    
D)  (5, -5); y = -3

Question 4

Solve.
-A carpenter wants to cut the largest possible ellipse from a 1 ft by 17 ft rectangular board. After the foci are located, a string is connected to them and pulled taut by a pencil in order to draw the ellipse. Find the length of
The string.

Accepted Answer

A)  17 ft 
B)  34 ft 
C)  1 ft 
D)  2 ft 
A)  17 ft 
B)  34 ft 
C)  1 ft 
D)  2 ft

Question 5

Find the new coordinates of the given point when the xy-coordinate system is rotated by the indicated angle.
-(5, 8); 60°

Accepted Answer

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

Question 6

Graph the hyperbola.
-

Accepted Answer

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

Question 7

Graph the parabola.
-

Accepted Answer

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

Question 8

Solve.
-A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 10 m down from the top of the dome the ceiling is 16 m wide, find the best location for
The light source.

Accepted Answer

A)  1.6 m down from the top 
B)  3.2 m down from the top 
C)  6.4 m down from the top 
D)  4.8 m down from the top 
A)  1.6 m down from the top 
B)  3.2 m down from the top 
C)  6.4 m down from the top 
D)  4.8 m down from the top

Question 9

Find the focus and the directrix of the parabola.
-

Accepted Answer

A)    
B)  (5, 0); x = -4 
C)  (5, 6); x = 10 
D)    
A)    
B)  (5, 0); x = -4 
C)  (5, 6); x = 10 
D)

Question 10

Identify the equation as a parabola, ellipse, or circle.
-

Accepted Answer

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

Question 11

Find the equation of the parabola with the given focus and directrix.
-

Accepted Answer

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

Question 12

Use the discriminant to determine whether the graph of the equation is an ellipse (or circle), a hyperbola, or a parabola.
-

Accepted Answer

A)  Ellipse/circle 
B)  Parabola 
C)  Hyperbola 
A)  Ellipse/circle 
B)  Parabola 
C)  Hyperbola

Question 13

Solve the problem.
-A circular pond is being installed in the corner of a yard, as shown. The installer needs to know the value of x in feet. Find x to the nearest tenth of a foot.   a = 38 ft

Accepted Answer

A)  0.8 ft 
B)  1.5 ft 
C)  1.1 ft 
D)  1.7 ft 
A)  0.8 ft 
B)  1.5 ft 
C)  1.1 ft 
D)  1.7 ft

Question 14

Solve.
-A building has an entry with the shape of a parabolic arch 14 ft high and 22 ft wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

Accepted Answer

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

Question 15

Find the new coordinates of the given point when the xy-coordinate system is rotated by the indicated angle.
-(3, 8); 45°

Accepted Answer

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

Question 16

Solve the problem. Round to the nearest tenth when necessary.
-A comet follows the hyperbolic path described by   where x and y are in millions of miles. If the sun is the focus of the path, how close to the sun is the vertex of the path?

Accepted Answer

A)  4.4 million mi 
B)  37 million mi 
C)  1.7 million mi 
D)  7.4 million mi 
A)  4.4 million mi 
B)  37 million mi 
C)  1.7 million mi 
D)  7.4 million mi

Question 17

Use the discriminant to determine whether the graph of the equation is an ellipse (or circle), a hyperbola, or a parabola.
-

Accepted Answer

A)  Parabola 
B)  Hyperbola 
C)  Ellipse/circle 
A)  Parabola 
B)  Hyperbola 
C)  Ellipse/circle

Question 18

Solve.
-A tunnel is in the shape of a parabola. The maximum height is 17 m and it is 7 m wide at the base. What is the vertical clearance 2 m from the edge of the tunnel?
A = 17 m
B = 7 m

Accepted Answer

A)  1.7 m 
B)  13.9 m 
C)  3.1 m 
D)  15.3 m 
A)  1.7 m 
B)  13.9 m 
C)  3.1 m 
D)  15.3 m

Question 19

Graph the hyperbola.
-

Accepted Answer

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

Question 20

Match the given graph with its equation.
-

Accepted Answer

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

Using the graph of the ellipse, determine the coordinates of the foci, vertices, and center. -

Find the coordinates of the vertex of the parabola. -

Find the focus and the directrix of the parabola. -

Solve. -A carpenter wants to cut the largest possible ellipse from a 1 ft by 17 ft rectangular board. After the foci are located, a string is connected to them and pulled taut by a pencil in order to draw the ellipse. Find the length of The string.

Find the new coordinates of the given point when the xy-coordinate system is rotated by the indicated angle. -(5, 8); 60°

Graph the hyperbola. -

Graph the parabola. -

Solve. -A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 10 m down from the top of the dome the ceiling is 16 m wide, find the best location for The light source.

Find the focus and the directrix of the parabola. -

Identify the equation as a parabola, ellipse, or circle. -

Find the equation of the parabola with the given focus and directrix. -

Use the discriminant to determine whether the graph of the equation is an ellipse (or circle), a hyperbola, or a parabola. -

Solve the problem. -A circular pond is being installed in the corner of a yard, as shown. The installer needs to know the value of x in feet. Find x to the nearest tenth of a foot. a = 38 ft

Solve. -A building has an entry with the shape of a parabolic arch 14 ft high and 22 ft wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

Find the new coordinates of the given point when the xy-coordinate system is rotated by the indicated angle. -(3, 8); 45°

Solve the problem. Round to the nearest tenth when necessary. -A comet follows the hyperbolic path described by where x and y are in millions of miles. If the sun is the focus of the path, how close to the sun is the vertex of the path?

Use the discriminant to determine whether the graph of the equation is an ellipse (or circle), a hyperbola, or a parabola. -

Solve. -A tunnel is in the shape of a parabola. The maximum height is 17 m and it is 7 m wide at the base. What is the vertical clearance 2 m from the edge of the tunnel? A = 17 m B = 7 m

Graph the hyperbola. -

Match the given graph with its equation. -

Equations, Inequalities, and Modeling

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Polynomial and Rational Functions

Exponential and Logarithmic Functions

The Trigonometric Functions

Trigonometric Identities and Conditional Equations

Applications of Trigonometry

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Matrices and Determinants

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Basic Algebra Review

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Exam 10: The Conic Sections

Using the graph of the ellipse, determine the coordinates of the foci, vertices, and center. -

Find the coordinates of the vertex of the parabola. -

Find the focus and the directrix of the parabola. -

Solve. -A carpenter wants to cut the largest possible ellipse from a 1 ft by 17 ft rectangular board. After the foci are located, a string is connected to them and pulled taut by a pencil in order to draw the ellipse. Find the length of The string.

Find the new coordinates of the given point when the xy-coordinate system is rotated by the indicated angle. -(5, 8); 60°

Graph the hyperbola. -

Graph the parabola. -

Solve. -A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 10 m down from the top of the dome the ceiling is 16 m wide, find the best location for The light source.

Find the focus and the directrix of the parabola. -

Identify the equation as a parabola, ellipse, or circle. -

Find the equation of the parabola with the given focus and directrix. -

Use the discriminant to determine whether the graph of the equation is an ellipse (or circle), a hyperbola, or a parabola. -

Solve the problem. -A circular pond is being installed in the corner of a yard, as shown. The installer needs to know the value of x in feet. Find x to the nearest tenth of a foot. a = 38 ft

Solve. -A building has an entry with the shape of a parabolic arch 14 ft high and 22 ft wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

Find the new coordinates of the given point when the xy-coordinate system is rotated by the indicated angle. -(3, 8); 45°

Solve the problem. Round to the nearest tenth when necessary. -A comet follows the hyperbolic path described by where x and y are in millions of miles. If the sun is the focus of the path, how close to the sun is the vertex of the path?

Use the discriminant to determine whether the graph of the equation is an ellipse (or circle), a hyperbola, or a parabola. -

Solve. -A tunnel is in the shape of a parabola. The maximum height is 17 m and it is 7 m wide at the base. What is the vertical clearance 2 m from the edge of the tunnel? A = 17 m B = 7 m

Graph the hyperbola. -

Match the given graph with its equation. -

Equations, Inequalities, and Modeling

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

The Trigonometric Functions

Trigonometric Identities and Conditional Equations

Applications of Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Sequences, Series, and Probability

Basic Algebra Review

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