WorksheetsParametric and Polar Equations
Total questions: 20
Worksheet time: 2hrs 6mins
Name
Class
Date
1.
Eliminate the parameter. Convert the parametric equation to rectangular. x= 2+4t and y=-1+6t
a)
y=(3/2)x - 4
b)
t=(x-2)/4
c)
y=x - 4
d)
y= (2/3)x + 4
2.
What curve do the parametric equations make? What is the direction of motion?
x=1+3sint
y=-2+4cost
x=1+3sint
y=-2+4cost
a)
Circle. Counterclockwise.
b)
Circle. Clockwise.
c)
Ellipse. Counterclockwise.
d)
Ellipse. Clockwise.
3.
What curve do the parametric equations make? What is the direction of motion?
x=1+3cost
y=-2+3sint
x=1+3cost
y=-2+3sint
a)
Circle. Counterclockwise.
b)
Circle. Clockwise.
c)
Ellipse. Counterclockwise.
d)
Ellipse. Clockwise.
4.
What is the center and radius of the curve:
x=1+3cost
y=-2+3sint
x=1+3cost
y=-2+3sint
a)
(-1,2) , r=3
b)
(-1,2) , r=9
c)
(1,-2) , r=3
d)
(1,-2) , r=9
5.
The coordinates of a car at time t are given by x = 8 - t and y = 2t - 16. As t increases, which direction and path is the car traveling?
a)
from left to right along the path y = 2x - 16.
b)
from left to right along the path y = 2x.
c)
from right to left along the path y = -2x.
d)
from left to right along the path y = -2x.
6.
Sketch the curve of x(t) = 2t + 1 and y(t) = t2 + 2.
a)
A
b)
B
c)
C
d)
D
7.
Eliminate the parameter from x(t) = t2 + 5 and y(t) = t2 - 4. Which of the following sketches results?
a)
Linear
b)
Quadratic
c)
Quartic
d)
Square Root
8.
Which set of parametric equations satisfies the given data table?
a)
x(t) = t3 - 1
y(t) = 2t
y(t) = 2t
b)
x(t) = t3 - 1
y(t) = t + 2
y(t) = t + 2
c)
x(t) = t + 8
y(t) = t + 2
y(t) = t + 2
d)
x(t) = t + 8
y(t) = 2t
y(t) = 2t
9.
Which point represents (3, 3π/4)?
a)
F
b)
E
c)
B
d)
A
10.
Which point represents the polar coordinate
(-4, -2π/3)?
(-4, -2π/3)?
a)
B
b)
F
c)
D
d)
A
11.
Which equation represents the polar graph?
a)
r = sin θ
b)
r = sin 4θ
c)
r = 4 sin θ
d)
r = 4 cos θ
12.
Converting parametric equations to a rectangular equation is called _________________ the parameter.
a)
eliminating
b)
finding
c)
converting
d)
jumping
13.
The parametric equation x = 3cos(t), y = 3sin(t) is a ..
a)
a circle
b)
an ellipse
c)
a hyperbolas
d)
parabola
14.
Eliminate the parameter. Convert the parametric equation to rectangular. x= t - 1 and y=t2 - 2
a)
y=(x+1)2 - 2
b)
t=x - 1
c)
x=t - 1
d)
y=t - 2
15.
Which t-step will graph the slowest?
a)
1
b)
.1
c)
.01
d)
.001
16.
Convert
a)
A
b)
B
c)
C
d)
D
17.
Kait hits the golfball at an angle of 27° with the horizontal at an initial speed of 22 m/s. How far has the ball traveled horizontally after 2 seconds?
a)
50.068 meters
b)
19.976 meters
c)
39.204 meters
d)
42.077 meters
18.
Alex hits the baseball at a 28° angle with an initial velocity of 103 feet per second. The ball is 4 feet off the ground (initial height) at time of impact. The ball is not caught by the outfielder and hits the ground. How far from home plate is the ball, approximately?
a)
282 ft.
b)
347 ft.
c)
188 ft.
d)
226 ft.
19.
Which half of the curve will be graphed for the parametric equation:
x=1+3cost
y=-2+4sint
π≤t≤2π
x=1+3cost
y=-2+4sint
π≤t≤2π
a)
Right half
b)
Left half
c)
Top half
d)
Bottom half
20.
Given the Rectangular Coordinate
(-7√2, 7√2), write the point as a polar coordinate for 0≤θ≤2π
(-7√2, 7√2), write the point as a polar coordinate for 0≤θ≤2π
a)
(14, π/4) , (-14, π/4)
b)
(14, 7π/4) , (14, π/4)
c)
(14, 5π/4) ,
(-14, 3π/4)
(-14, 3π/4)
d)
(-14, 7π/4),
(14, 3π/4)
(14, 3π/4)
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