Question 1

Which of the following sets of parametric equations is equivalent to   ?

Accepted Answer

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

Question 2

Find all points at which the two curves intersect.   and

Accepted Answer

A)    where   is any integer 
B)    where   is any integer 
C)    where   is any integer,   where   is any integer 
D)    where   is any integer,   where   is any integer 
A)    where   is any integer 
B)    where   is any integer 
C)    where   is any integer,   where   is any integer 
D)    where   is any integer,   where   is any integer

Question 3

For the given parametric equations, find a corresponding x-y equation for the curve.

Accepted Answer

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

Question 4

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5].

Accepted Answer

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

Question 5

Parametric equations for the position of an object are given. Find the object's velocity and speed at the given time.

Accepted Answer

A)  horizontal component of velocity: 0 vertical component of velocity: 9
Speed: 9 
B)  horizontal component of velocity: -7 vertical component of velocity: 0
Speed: 7 
C)  horizontal component of velocity: 7 vertical component of velocity: 0
Speed: -7 
D)  horizontal component of velocity:   vertical component of velocity:  
Speed:   
A)  horizontal component of velocity: 0 vertical component of velocity: 9
Speed: 9 
B)  horizontal component of velocity: -7 vertical component of velocity: 0
Speed: 7 
C)  horizontal component of velocity: 7 vertical component of velocity: 0
Speed: -7 
D)  horizontal component of velocity:   vertical component of velocity:  
Speed:

Question 6

The tires on an automobile have a radius of 0.36 meters. If the tires make 11 revolutions per second, find the speed of the car in kilometers per hour (kph). Round to the nearest tenth. [1 km = 1000 m and 1 hr = 3600 s]

Accepted Answer

A)  89.6 kph 
B)  44.8 kph 
C)  14.3 kph 
D)  28.5 kph 
A)  89.6 kph 
B)  44.8 kph 
C)  14.3 kph 
D)  28.5 kph

Question 7

Find the arc length of the curve. Approximate numerically, if needed.

Accepted Answer

A)  30 
B)  15 
C)  30$\pi$ 
D)  5$\pi$ 
A)  30 
B)  15 
C)  30$\pi$ 
D)  5$\pi$

Question 8

Identify a range of values of   that produces one copy of the graph.

Accepted Answer

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

Question 9

Find a corresponding x-y equation. r = 5

Accepted Answer

A)    
B)  x2 + y2 = 25 
C)    
D)  x2 + y2 = 5 
A)    
B)  x2 + y2 = 25 
C)    
D)  x2 + y2 = 5

Which of the following sets of parametric equations is equivalent to ?

Find all points at which the two curves intersect. and

For the given parametric equations, find a corresponding x-y equation for the curve.

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5].

Parametric equations for the position of an object are given. Find the object's velocity and speed at the given time.

The tires on an automobile have a radius of 0.36 meters. If the tires make 11 revolutions per second, find the speed of the car in kilometers per hour (kph). Round to the nearest tenth. [1 km = 1000 m and 1 hr = 3600 s]

Find the arc length of the curve. Approximate numerically, if needed.

Identify a range of values of that produces one copy of the graph.

Find a corresponding x-y equation. r = 5

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 11: Parametric Equations and Polar Coordinates

Which of the following sets of parametric equations is equivalent to ?

Find all points at which the two curves intersect. and

For the given parametric equations, find a corresponding x-y equation for the curve.

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5].

Parametric equations for the position of an object are given. Find the object's velocity and speed at the given time.

The tires on an automobile have a radius of 0.36 meters. If the tires make 11 revolutions per second, find the speed of the car in kilometers per hour (kph). Round to the nearest tenth. [1 km = 1000 m and 1 hr = 3600 s]

Find the arc length of the curve. Approximate numerically, if needed.

Identify a range of values of that produces one copy of the graph.

Find a corresponding x-y equation. r = 5

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters