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Unit 12 Circles in a Coordinate Plane Test Review - Printable Mathematics Worksheets class 9 - Wayground

Unit 12 Circles in a Coordinate Plane Test Review

20 questions

9th - 12th Grade

Mathematics

Unit 12 Circles in a Coordinate Plane Test Review is a 20-question mathematics worksheet for students in Grades 9–12. It reviews how to interpret circle diagrams and solve for unknown values involving circumscribed polygons, radii, tangents, chords, secants, intercepted arcs, and angle measures. Students also write standard-form equations for circles from a center and radius, including circles centered at the origin and at a given coordinate. The review uses varied item types—dropdown questions, drag-and-drop diagram tasks, multiple-choice questions, math responses, and a matching item—so students demonstrate both procedural fluency and diagram-based reasoning. It is useful for independent practice, test preparation, reteaching, or a unit review on circles in the coordinate plane. This free printable worksheet includes a complete answer key for efficient checking and feedback.

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Unit 12 Circles in a Coordinate Plane Test Review

Total questions: 20

Name
Class
Date
1.

The polygon circumscribes a circle. What is the perimeter of the polygon? (a)  

Choose from the below words
78 cm
39 cm
5320 cm
13 cm
2.

In the figure to the right, if AC = 16 and BC = 13, what is the radius? Round to the nearest tenth. (a)  

Choose from the below words
9.3 units
87 units
9.2 units
3 units
3.

Determine whether a tangent is shown in the diagram. (a)  

Choose from the below words
Yes
No
4.
a)

20 degrees

b)

40 degrees

c)

60 degrees

d)

10 degrees

5.

Find the value of x.

6.

Find the value of x. Round to the nearest tenth. (a)  

Choose from the below words
5.1 units
26.2 units
74.24 units
8.6 units
7.

Find the value of a°a^{\degree} . The dot represents the center of the circle.

8.

What arc does angle F intercept?

a)

b)

c)

d)

e)

9.
Question Image

Find the value of each variable. Match the variable to its correct value.

58.5°58.5^{\degree}

a

90°90^{\degree}

b

63°63^{\degree}

c

10.

Find the value of x. Round to the nearest tenth.

a)

32

b)

3.2

c)

12

d)

320

11.

Find the values of x and y. Lines that appear tangent are tangent.

x (a)  

y (b)  

​

Choose from the below words

60°60^{\degree}  

120°120^{\degree}  

12.

Find the value of angle y.

a)

59°59^{\degree}

b)

41.5°41.5^{\degree}

c)

118°118^{\degree}

13.

Find the value of angle z.

a)

82°82^{\degree}

b)

41°41^{\degree}

c)

62°62^{\degree}

d)

144144^{ }

14.

Find the value of c using the given chord and secant lengths in the diagram shown to the left. Round answer to nearest tenth.

a)

14.9

b)

23.6

c)

2.1

d)

8.1

15.

Write the standard equation for the circle

whose center is at (7,1) and whose radius is at 4.

a)

(x−7)2+(y−1)2=16\left(x-7\right)^2+\left(y-1\right)^2=16

b)

(x+7)2+(y+1)2=4\left(x+7\right)^2+\left(y+1\right)^2=4

c)

(x+7)2+(y+1)2=16\left(x+7\right)^2+\left(y+1\right)^2=16

d)

(x−7)2−(y+1)2=4\left(x-7\right)^2-\left(y+1\right)^2=4

16.

Write the standard form of the equation of the circle with the given center and radius.

Center​ (0,0), r=10

a)

x2+y2=10x^2+y^2=10

b)

x2+y2=100x^2+y^2=100

c)

x2−y2=10x^2-y^2=10

d)

x2−y2=100x^2-y^2=100

17.

Write the standard form of the equation of the circle with its center at (−1,0)​, and a radius of 6.

a)

(x+1)2+y2=36\left(x+1\right)^2+y^2=36

b)

(x+1)2−y2=36\left(x+1\right)^2-y^2=36

c)

(x−1)2+y2=6\left(x-1\right)^2+y^2=6

d)

(x+1)2+(y+1)2=36\left(x+1\right)^2+\left(y+1\right)^2=36

18.

What is the center of the following equation:

(x−1)2+y2=36\left(x-1\right)^2+y^2=36

a)

(1,0)

b)

(-1,0)

c)

(0,1)

d)

(0,-1)

19.

What is the radius of the following equation:

(x−1)2+y2=36\left(x-1\right)^2+y^2=36

a)

6

b)

36

c)

1

d)

-1

20.

Write the standard form of the equation of the circle to the left.

a)

(x−1)2+(y−1)2=7\left(x-1\right)^2+\left(y-1\right)^2=7

b)

(y−1)2+(y−1)2=49\left(y-1\right)^2+\left(y-1\right)^2=49

c)

(y+1)2+(y+1)2=49\left(y+1\right)^2+\left(y+1\right)^2=49

Answer Key

Unit 12 Circles in a Coordinate Plane Test Review

Total questions: 20

1.
78 cm
2.
9.3 units
3.
No
4.
a)

20 degrees

5.

1818

6.
5.1 units
7.

150150

8.
e)
9.

58.5°58.5^{\degree}

 - 

a

, 

90°90^{\degree}

 - 

b

, 

63°63^{\degree}

 - 

c

10.
b)

3.2

11.

60°60^{\degree}  

,

120°120^{\degree}  

12.
a)

59°59^{\degree}

13.
b)

41°41^{\degree}

14.
b)

23.6

15.
a)

(x−7)2+(y−1)2=16\left(x-7\right)^2+\left(y-1\right)^2=16

16.
b)

x2+y2=100x^2+y^2=100

17.
a)

(x+1)2+y2=36\left(x+1\right)^2+y^2=36

18.
b)

(-1,0)

19.
a)

6

20.
c)

(y+1)2+(y+1)2=49\left(y+1\right)^2+\left(y+1\right)^2=49

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FAQs

What does the Unit 12 Circles in a Coordinate Plane Test Review worksheet cover?

This 20-question review covers circle geometry and coordinate-plane skills, including finding radii and unknown variables, identifying tangents, using chord and secant lengths, determining intercepted arcs and angle measures, and writing standard-form equations of circles. Its dropdown, drag-and-drop, multiple-choice, math-response, and matching items require students to apply these relationships in diagrams as well as with coordinates and formulas.

How can I use this worksheet to teach circles in a coordinate plane?

Use the diagram-based items to model how students identify the circle’s center, radius, tangent, chord, secant, and intercepted arc before they calculate unknown values. Then have students complete the equation questions by connecting a circle’s center and radius to standard form, and ask them to explain why a selected value or rounded answer is reasonable.

What mistakes should I watch for when students complete this circles review?

Watch for students confusing a radius with a diameter, accepting a line as tangent without checking its relationship to the circle, or matching an angle with the wrong intercepted arc. Students may also substitute center coordinates incorrectly in the standard-form equation, skip the chord-and-secant relationship, or round numerical answers before completing the calculation.

How do I assign and grade this circles worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key. You can grade printable submissions by scanning student work with the Wayground for Teachers app, or review responses from the digital version.

How can I differentiate this circles review worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing and font size to make the circle diagrams, equations, and response areas easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when that support is useful for students working through the geometry terminology.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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