NEW
Font size
S
M
L
XL
WorksheetsPolar Quiz Review
Total questions: 35
Worksheet time: 6hrs 37mins
Name
Class
Date
1.
Which point represents (3, 3π/4)
a)
F
b)
E
c)
B
d)
A
2.
Which point represents the polar coordinate
(-2, -5π/6)
(-2, -5π/6)
a)
B
b)
F
c)
D
d)
C
3.
Which point represents the polar coordinate
(-4, -2π/3)
(-4, -2π/3)
a)
B
b)
F
c)
D
d)
A
4.
Which of these coordinates do not belong?
a)
(4, -150o)
b)
(-4, -210o)
c)
(4, 690o)
d)
(4,-30o)
5.
Which equation represents the polar graph?
a)
r = 6 + 6 sin θ
b)
r = 12 sin θ
c)
r = 4 - 3 sin θ
d)
r = 4 + 5 sin θ
6.
Convert
a)
A
b)
B
c)
C
d)
D
7.
Convert the rectangular coordinates to polar form
a)
(√2 , 315o)
b)
(2 , 135o)
c)
(4 , 45o)
d)
(4 , 225o)
8.
Convert the polar coordinates to rectangular form
a)
( -3, 3)
b)
(3, 3√3)
c)
(-3, 3√3)
d)
(3, -3√3)
9.
Convert the polar equation to rectangular form
a)
x² + y² = 49
b)
x = 7
c)
x + y = 49
d)
x² + y² = 7
10.
Covert the rectangular equation to polar form
a)
r sin θ = 4
b)
r = 4 csc θ
c)
4 = 4 sec θ
d)
4 = r cos θ
11.
Convert θ = 225o to rectangular equation
a)
y= -x
b)
y = x
c)
tanθ=-1
d)
tanθ=1
12.
Describe the curve
a)
Rose with 3 leaves
b)
Rose with 6 leaves
c)
Inner loop limacon
d)
Circle
13.
Describe the curve
a)
Rose with 3 leaves
b)
Circle
c)
Cardioid
d)
Inner loop limacon
14.
Describe the curve
a)
Circle
b)
Cardioid
c)
Inner loop limacon
d)
Dimpled limacon
15.
Which equation represents the polar graph?
a)
r = sin 4θ
b)
r = 6 sin 2θ
c)
r = 6 cos 2θ
d)
r = cos 4θ
16.
Which equation represents the polar graph?
a)
r = sin θ
b)
r = sin 4θ
c)
r = 4 sin θ
d)
r = 4 cos θ
17.
If z = 2(cos(20) + isin(20)) and w = 3(cos(105) + isin(105)), find z / w
a)
2/3(cos(-85) + isin(-85))
b)
2/3(cos(275) + isin(275))
c)
3/2(cos(85) + isin(85))
d)
6(cos(125) + isin(125))
18.
Which are possible coordinates of the point graphed?
a)
(-2, 120o)
b)
(-2, 60o)
c)
(2, -120o)
d)
(2, 60o)
19.
This particular equation generates what graph
a)
b)
c)
d)
20.
Choose the correct equation.
a)
r = 3 + 2 cosθ
b)
r = 2 + 3 cosθ
c)
r = 2 + 2cosθ
d)
r = 3cosθ
21.
Choose a correct equation for this rose curve.
a)
r = sin(7θ)
b)
r = 7sin(2θ)
c)
r = 2sin(7θ)
d)
r = 2sin(14θ)
22.
Find
5(cos 2π /3 + i sin 2π /3)⋅2( cos π /3 + i sin π /3)
in polar form. Then express your final answer in rectangular form.
5(cos 2π /3 + i sin 2π /3)⋅2( cos π /3 + i sin π /3)
in polar form. Then express your final answer in rectangular form.
a)
-10
b)
10
c)
-10i
d)
10i
23.
Find
1/2 ( cos π /3 + i sin π /3)
÷ 3 ( cos π /6 + i sin π /6)
and express your final answer in rectangular form.
1/2 ( cos π /3 + i sin π /3)
÷ 3 ( cos π /6 + i sin π /6)
and express your final answer in rectangular form.
a)
√3/12 + 1/12 i
b)
12√3 + 12 i
c)
√3/12 - 1/12 i
d)
12√3 - 12i
24.
The polar complex form of -2 + 2√3i is:
a)
z =2(cos(120) + isin(120))
b)
z =4(cos(120) + isin(120))
c)
z=2(cos(300))+isin(300))
d)
z=4(cos(300))+isin(300))
25.
Write the equation of a limacon with an inner loop of length 3 and an outer loop of length 7, symmetric to the π/2 axis.
a)
r = 2 + 5sin(θ)
b)
r = 3 + 7sin(θ)
c)
r = 2 - 5cos(θ)
d)
r = 3 - 7cos(θ)
26.
If z = 2(cos(20) + isin(20)) and w = 3(cos(105) + isin(105)), find z ⋅ w
a)
3/2(cos(85) + isin(85))
b)
3/2(cos(125) + isin(125))
c)
6(cos(85) + isin(85))
d)
6(cos(125) + isin(125))
27.
Given the polar point (6, π/9), find an equivalent polar point using a negative angle.
a)
(6, -π/9)
b)
(6, -17π/9)
c)
(6, -10π/9)
d)
(-6, -π/9)
28.
What quadrant would the point in standard form land in?
4 ( cos π /3 + i sin π /3)
4 ( cos π /3 + i sin π /3)
a)
Quadrant 4
b)
Quadrant 1
c)
Quadrant 2
d)
Quadrant 3
29.
Convert the polar equation to rectangular form
a)
x = 2 cos θ
b)
x = 2
c)
y = 2
d)
x² + y² = 2
30.
Convert the polar equation to rectangular form
a)
y = x
b)
x = 0
c)
y = 0
d)
tan θ = 0
31.
Match the correct polar equation with the following graph:
a)
r=1+cosθ
b)
rsinθ=2
c)
r=1-2sinθ
d)
r=2
32.
Choose a correct equation for the red circle.
a)
r = -3
b)
r = -3sinΘ
c)
r = -3cosΘ
d)
x² + y² = 3
33.
What interval will give you the shaded region given?
a)
0 ≤ θ ≤ π/2
b)
0 ≤ θ ≤ π
c)
π/2 ≤ θ ≤ π
d)
π ≤ θ ≤ 2π
34.
What interval will give the given shaded region?
a)
π/5 ≤ θ ≤ 2π/5
b)
2π/5 ≤ θ ≤ 3π/5
c)
3π/5 ≤ θ ≤ 4π/5
d)
4π/5 ≤ θ ≤ π
e)
0 ≤ θ ≤ π/5
35.
Convert the polar equation to rectangular form.
r=−4sinθ
a)
(x−2)2+(y−1)2=5
b)
(x−1)2+(y−3)2=10
c)
(x+1)2+(y−2)2=5
d)
x2+(y+2)2=4
Reset
