Free Printable Polar Graphs Mastery Quiz

1.

What is the name of the polar graph represented by the equation $r = 1 + \sin(\theta)$ ?

a)

Limaçon

b)

Circle

c)

Lemniscate

d)

Rose

2.

Which of the following equations represents a circle in polar coordinates?

a)

$r = 2\cos(\theta)$

b)

$r = 1 - \sin(\theta)$

c)

$r = 2$

d)

$r = 2\sin(2\theta)$

3.

How would the polar coordinates $(3, \frac{\pi}{2})$ be converted to rectangular coordinates?

a)

$(0, 3)$

b)

$(3, 0)$

c)

$(-3, 0)$

d)

$(0, -3)$

4.

What is the graph of the polar equation $r = 2\sin(2\theta)$ known as?

a)

Circle

b)

Limaçon

c)

Lemniscate

d)

Rose

5.

If a polar equation is given by $r = 4\cos(\theta)$ , what type of graph does it produce?

a)

Circle

b)

Ellipse

c)

Limaçon

d)

Rose

6.

Convert the rectangular coordinates $(\sqrt{3}, 1)$ to polar coordinates.

a)

$(2, \frac{\pi}{6})$

b)

$(2, \frac{\pi}{3})$

c)

$(2, \frac{5\pi}{6})$

d)

$(2, \frac{\pi}{4})"

7.

What is the name of the polar graph represented by the equation $r = \cos(2\theta)$ ?

a)

Circle

b)

Limaçon

c)

Lemniscate

d)

Rose

8.

How would the polar coordinates $(4, \pi)$ be converted to rectangular coordinates?

a)

$(4, 0)$

b)

$(-4, 0)$

c)

$(0, 4)$

d)

$(0, -4)$

9.

What is the graph of the polar equation $r = 3\cos(\theta)$ known as?

a)

Circle

b)

Limaçon

c)

Lemniscate

d)

Rose

10.

Convert the rectangular coordinates $(2, \sqrt{2})$ to polar coordinates.

a)

$(2\sqrt{2}, \frac{\pi}{4})$

b)

$(2\sqrt{2}, \frac{\pi}{2})$

c)

$(2\sqrt{2}, \frac{3\pi}{4})$

d)

$(2\sqrt{2}, \pi)$

11.

How would the polar coordinates $(5, \frac{2\pi}{3})$ be converted to rectangular coordinates?

a)

$(-2.5, 4.33)$

b)

$(2.5, -4.33)$

c)

$(-2.5, -4.33)$

d)

$(2.5, 4.33)$

12.

Convert the rectangular coordinates $(1, 2)$ to polar coordinates.

a)

$(\sqrt{5}, \arctan(2))$

b)

$(2, \arctan(0.5))$

c)

$(\sqrt{5}, \arctan(0.5))$

d)

$(2, \arctan(2))$

13.

How would the polar coordinates $(2, \frac{\pi}{4})$ be converted to rectangular coordinates?

a)

$(\sqrt{2}, \sqrt{2})$

b)

$(-\sqrt{2}, \sqrt{2})$

c)

$(\sqrt{2}, -\sqrt{2})$

d)

$(-\sqrt{2}, -\sqrt{2})$

14.

Which point represents (2, π/6)

a)

F

b)

E

c)

B

d)

A

15.

Convert the polar coordinates to rectangular form

a)

( -3, 3)

b)

(3, 3√3)

c)

(-3, 3√3)

d)

(3, -3√3)

16.

How do you write an ordered pair in polar coordinates?

a)

(X, Y)

b)

(θ, r)

c)

(r,θ)

d)

(Y_Y)

17.

Find the rectangular coordinates of each polar point. (4, 3π/2)

a)

(4,4)

b)

(4,0)

c)

(0,-4)

d)

(0,1)

18.

Convert the rectangular equation to polar form

a)

r² = 81

b)

r = 3

c)

r = 4.5

d)

r sin θ = 9

19.

Which point describes the location of the following graph.

a)

$\left(5,300\degree\right)$

b)

$\left(-5,330\degree\right)$

c)

$\left(-5,300\degree\right)$

20.

Check ALL of the coordinate sets that give the same resulting point as $\left(7,\frac{\pi}{3}\right)$ .

a)

$\left(-7,\frac{4\pi}{3}\right)$

b)

$\left(-7,-\frac{2\pi}{3}\right)$

c)

$\left(-7,-\frac{\pi}{3}\right)$

d)

$\left(7,-\frac{5\pi}{3}\right)$

21.

Change the following coordinates from rectangular to polar. $\left(1,\ -\sqrt{3}\right)$

a)

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

b)

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

c)

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

d)

$\left(2,\ \frac{11\pi}{6}\right)$

22.

Write the polar equation into a rectangular equation?
r=2sinΘ+2cosΘ

a)

x²+y²=2x+2y

b)

r=2x+2y

c)

r=x²+y²

d)

x²-y²=2x-2y

23.

Write the polar equation into a rectangular equation?
r=sinΘ

a)

x²+y²=y

b)

y=x²

c)

1=x²+y²

d)

x²+y²=2x+2y

24.

Which of the following are the coordinates of the point.

a)

$\left(4,\ -\frac{5\pi}{4}\right)$

b)

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

c)

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

d)

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

25.

In the coordinate points (2,7⁰) the 2 represents the...

a)

theta

b)

radius

c)

x

d)

angle

26.

Which point represents (5, π)

a)

F

b)

E

c)

B

d)

A

27.

Find the polar coordinates of the rectangular point. (-3,0)

a)

(3,π)

b)

(3,0)

c)

(3,π/2)

d)

(3,-3π/2)

28.

Find the polar coordinates of the rectangular point. (0,3)

a)

(3,π)

b)

(3,0)

c)

(3,π/2)

d)

(3,-3π/2)

29.

Convert from polar to rectangular:

(5, 135^o)

a)

(-5√2/2, 5√2/2)

b)

(5√2/2, 5√2/2)

c)

(5√2/2, -5√2/2)

d)

(-5√2/2, -5√2/2)

30.

What is the radius to the following rectangular point:

(5, 2)

a)

5

b)

2

c)

√29

d)

√27

31.

What are the polar coordinates for the point (6, 6)?

a)

(√24, 90°)

b)

(√72, 45°)

c)

(10, 60°)

d)

(8, 30°)

32.

Find the polar coordinates for the point (4, -3).

a)

(3, 45°)

b)

(4, -53.13°)

c)

(6, 120°)

d)

(5, -36.87°)

33.

If the rectangular coordinates are (9, -12), what are the polar coordinates?

a)

(15, 126.87°)

b)

(9, -12)

c)

(15, 53.13°)

d)

(21, 45°)

34.

If the polar equation is $r\ =5$ , what is the rectangular equaiton?

a)

$x\ +y=5$

b)

$r=5\cos\theta$

c)

$x^2+y^2=25$

d)

$\tan\theta=5$

35.

Do the rectangular points (3, -2) and (3, 2) have the same polar coordinates? Choose the best answer.

a)

yes, because you square the x and y values.

b)

no, the r values will be the same but angle theta will be different because the points are in different quadrants.

c)

no, both r and angle theta are different.

36.

How do we find values for $\cos\theta\ \ and\ \ \ \sin\theta$ ?

a)

We look at our trusty unit circle!

b)

We take a wild guess.

37.

Covert the rectangular equation to polar form $y=x^2$

a)

r = cot θ csc θ

b)

r = tan θ csc θ

c)

r = tan θ sec θ

d)

r = 0

38.

Covert the rectangular equation to polar form $x^2+y^2=9$

a)

r² = 81

b)

r = 3

c)

r = 4.5

d)

r sin θ = 9

39.

Convert the polar coordinates to rectangular form $\left(\sqrt{2},\ -\frac{\pi}{4}\right)$

a)

(1, 1)

b)

(1, -1)

c)

(-1, 0)

d)

(-1, -1)

40.

a)

A

b)

B

c)

C

d)

D

Polar Graphs Mastery Quiz

Total questions: 40

Worksheet time: 2hrs 29mins

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