Free Printable G11 Polar Graphs and Equations

1.

Match the correct polar equation with the following graph:

a)

r=1+cosθ

b)

rsinθ=2

c)

r=1-2sinθ

d)

r=2

2.

Identify the polar equation:
r=1+sinθ

a)

cardioid

b)

circle

c)

limacon with inner loop

d)

spiral

3.

Which point represents (2, π/6)

a)

F

b)

E

c)

B

d)

A

4.

Which of the following could be the equation for...

a)

r = 6 + 6 sin θ

b)

r = 12 sin θ

c)

r = 6 - 6 sin θ

d)

r = 6 + 6 cos θ

5.

Choose a correct equation for the red circle.

a)

r = -3

b)

r = -3sinΘ

c)

r = -3cosΘ

d)

x² + y² = 3

6.

Choose a correct equation for the blue circle.

a)

r = 2

b)

r = 4

c)

r = 2sinΘ

d)

x² + y² = 2

7.

Choose the correct equation.

a)

r = 3 + 2 cosθ

b)

r = 2 + 3 cosθ

c)

r = 2 + 2cosθ

d)

r = 3cosθ

8.

What is the equation?

a)

Θ = π/4

b)

Θ = -5π/4

c)

Θ = -3π/4

d)

Θ = 5π/4

9.

Identify the polar equation:
r=4sin(5θ)

a)

rose

b)

lemniscate

c)

spiral

d)

circle

10.

Which point represents (5, π)

a)

F

b)

E

c)

B

d)

A

11.

Describe the curve.

a)

Rose with 4 leaves, Length 4

b)

Rose with 8 leaves, Length 4

c)

Cardioid with length 3

d)

Inner loop limacon with lengths 3 and 4

12.

Describe the curve.

a)

Circle facing up with length 3

b)

Circle facing down with length 3

c)

Cardioid facing up with length 3

d)

Cardioid facing down with length 3

13.

Determine the polar equation of the given graph.

a)

r² = -9sin(2θ)

b)

r² = 9cos(2θ)

c)

r² = -9cos(2θ)

d)

r² = 9sin(2θ)

14.

Describe the curve

a)

Circle

b)

Cardioid

c)

Rose with 5 leaves

d)

Rose with 9 leaves

15.

The graph is an example of

a)

Spiral of Archimedes

b)

Logarithmic Spiral

c)

Spiral of Antiquity

d)

Limax Spiral

16.

What is the equation for this graph?

a)

r² = 9cos2θ

b)

r² = 9sin2θ

c)

r² = 3cosθ

d)

r² = 3sinθ

17.

How do you write an ordered pair in polar coordinates?

a)

(X, Y)

b)

(θ, r)

c)

(r,θ)

d)

(Y_Y)

18.

Which of these is an equation for this dimpled limaçon?

a)

r = 3 + 2 cosθ

b)

r = 2 + 3 cosθ

c)

r = 2 + 2cosθ

d)

r = 2 - 3cosθ

19.

Identify the polar equation:
r=1-3cosθ

a)

Limacon with inner loop

b)

Limacon without inner loop

c)

rose

d)

spiral

20.

Identify the polar equation:
r=1-3cosθ

a)

Limacon with inner loop

b)

Limacon without inner loop

c)

rose

d)

spiral

21.

What is the equation?

a)

r = 4

b)

r = 8

c)

r = 4sin(Θ)

d)

r = 8sin(Θ)

22.

What is the equation?

a)

r = 4sin(Θ)

b)

r = -2sin(Θ)

c)

r = 2cos(Θ)

d)

r = -4cos(Θ)

23.

The graph of r = 3 - 5cos(Θ) is a limacon with an inner loop. What is the diameter of the outer and inner loops?

a)

Outer Loop: 8, Inner Loop: 2

b)

Outer Loop: 4, Inner Loop: 1

c)

Outer Loop: 16, Inner Loop: 4

d)

Outer Loop: 15, Inner Loop: 2

24.

What kind of graph will you get from r = 2 + 6cos(Θ)?

a)

A limacon with an inner loop

b)

A dimpled limacon

c)

A cardiod (heart)

d)

A circle

25.

What kind of graph will you get from r = 2 + 6cos(Θ)?

a)

A limacon with an inner loop

b)

A dimpled limacon

c)

A cardiod (heart)

d)

A circle

26.

What kind of graph will you get from the equation r = 6 + 2cos(Θ)?

a)

A limacon with an inner loop

b)

A dimpled limacon

c)

A cardiod

d)

A line

27.

What kind of graph will you get from the equation r = 2 + 2cos(Θ)?

a)

A limacon with an inner loop

b)

A dimpled limacon

c)

A cardiod

d)

A flower

28.

What is the difference between the polar graphs of r = 2 + 6cos(Θ) and

r = 2 - 6cos(Θ)?

a)

Both are on the x-axis, but one faces right while the other faces left

b)

Both are on the y-axis, but one faces up while the other faces down

c)

One is on the x-axis while the other is on the y-axis

d)

They are the same!

29.

This particular equation generates what graph

a)

b)

c)

d)

30.

Which equation represents the polar graph?

a)

r = sin 4θ

b)

r = 6 sin 2θ

c)

r = 6 cos 4θ

d)

r = cos 4θ

31.

Choose a correct equation for this rose curve.

a)

r = sin(7θ)

b)

r = 7sin(2θ)

c)

r = 2sin(7θ)

d)

r = 2sin(14θ)

32.

Identify the polar equation:

r = 4sin(5θ)

a)

rose

b)

lemniscate

c)

spiral

d)

circle

33.

Identify the polar equation:

r² = 9cos(2θ)

a)

lemniscate

b)

limacon with inner loop

c)

cardioid

d)

rose

34.

Describe the curve

a)

Cardioid

b)

Circle

c)

Inner loop limacon

d)

Rose with 6 leaves

35.

The following equation would graph what shape?

a)

3 leaf rose

b)

6 leaf rose

c)

2 leaf rose

d)

4 leaf rose

36.

Which equation below generates this particular graph?

a)

b)

c)

d)

37.

Determine the polar equation of the given graph.

a)

r² = -9sin(2θ)

b)

r² = 9cos(2θ)

c)

r² = -9cos(2θ)

d)

r² = 9sin(2θ)

38.

The polar coordinate system is based on a point, called the ______ and a ray, called the _______ axis.

a)

pole, polar

b)

radius, x

c)

pole, x

d)

radias, polar

39.

Which of the following are the coordinates of the point.

a)

$\left(4,\ \frac{7\pi}{4}\right)$

b)

$\left(4,\ \frac{3\pi}{4}\right)$

c)

$\left(-4,\ \frac{3\pi}{4}\right)$

d)

$\left(-4,\ -\frac{\pi}{4}\right)$

40.

Which of the following are the coordinates of the point.

a)

$\left(2,\ \frac{11\pi}{12}\right)$

b)

$\left(-2,\ \frac{13\pi}{12}\right)$

c)

$\left(2,\ -\frac{13\pi}{12}\right)$

d)

$\left(2,\ \frac{13\pi}{12}\right)$

41.

Which of the following are the coordinates of the point.

a)

$\left(5,\ -\frac{2\pi}{3}\right)$

b)

$\left(-5,\ \frac{2\pi}{3}\right)$

c)

$\left(5,\ \frac{2\pi}{3}\right)$

d)

$\left(5,\ -\frac{\pi}{3}\right)$

G11 Polar Graphs and Equations

Total questions: 41

Worksheet time: 6hrs 3mins

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