Name: ________________________ Class: ___________________ Date: __________
ID: A
Module 12 Practice Quiz
Matching
Match each vocabulary term with its definition.
a. adjacent arcs
e.
b. arc
f.
c. arc length
g.
d. congruent arcs
h.
segment of a circle
major arc
intercepted arc
semicircle
____
1. a region inside a circle bounded by a chord and an arc
____
2. two arcs that are in the same or congruent circles and have the same measure
____
3. two arcs of the same circle that intersect at exactly one point
____
4. an arc of a circle whose points are on or in the exterior of a central angle
____
5. an unbroken part of a circle consisting of two points on the circle called the endpoints and all the points of the
circle between them
Match each vocabulary term with its definition.
a. chord
e.
b. arc
f.
c. point of tangency
g.
d. secant
h.
tangent of a circle
interior of a circle
common tangent
exterior of a circle
____
6. a line that is in the same plane as a circle and intersects the circle at exactly one point
____
7. a line that intersects a circle at two points
____
8. a line that is tangent to two circles
Match each vocabulary term with its definition.
a. subtend
e.
b. tangent circles
f.
c. arc length
g.
d. congruent circles
____
sector of a circle
inscribed angle
intercepted arc
9. a region inside a circle bounded by two radii of the circle and their intercepted arc
Match each vocabulary term with its definition.
a. interior of a circle
e.
b. tangent circles
f.
c. concentric circles
g.
d. congruent circles
h.
____ 10. an angle whose vertex is the center of a circle
1
central angle
subtend
tangent circles
minor arc
Name: ________________________
ID: A
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Find BD .
a.
b.
____
c.
d.
BD = 5
BD = 10
2. Find the arc length of an arc with measure 130° in a circle with radius 2 in. Round to the nearest tenth.
a.
b.
____
BD = 16
BD = 8
4.5 in
2.3 in
c.
d.
10.2 in
0.5 in
3. WX  YZ . Find mWX .
a.
mWX = 17
c.
mWX = 1
b.
mWX = 5
d.
mWX = 23
2
Name: ________________________
____
4. Convert 25 to radians.
a. 25

b.
____
c.
d.
5
36
5
72
5. Find the point of tangency and write the equation of the tangent line at this point.
a.
b.
c.
d.
____
25
ID: A
point of tangency: B(3,
point of tangency: B(3,
point of tangency: C(2,
point of tangency: A(0,
0) ; equation of the tangent line: x  3
0) ; equation of the tangent line: y  3
0); equation of the tangent line: x  y  3
0) ; equation of the tangent line: y  x  3
6. Find the area of sector POM. Give your answer in terms of  .
a.
b.
2.4 cm 2
0.6 cm 2
c.
d.
3
864 cm 2
1.2 cm 2
Name: ________________________
ID: A
____
7. Carlos has a collection of old vinyl records. To play some of the records, the turntable rotates through an
angle of 3 radians in 1 second. How many revolutions does the record make in one minute?
2
c. 78 revolutions per minute
a. 33 1 revolutions per minute
3
b. 45 revolutions per minute
d. 16 2 revolutions per minute
3
____
8. Jenny’s birthday cake is circular and has a 30 cm radius. Her slice creates an arc with a central angle of 120.
What is the area of Jenny’s slice of cake? Give your answer in terms of  .
c. 150 cm 2
a. 300 cm 2
b. 10 cm 2
d. 3600 cm 2
____
9. Convert 17 from radians to degrees.
10
a. 366°
b. 306°
c.
d.
4
279°
252°
ID: A
Module 12 Practice Quiz
Answer Section
MATCHING
1. ANS:
REF:
DOK:
2. ANS:
REF:
TOP:
3. ANS:
REF:
DOK:
4. ANS:
DOK:
5. ANS:
REF:
TOP:
E
PTS: 1
DIF:
1d28c4ae-4683-11df-9c7d-001185f0d2ea
DOK 1
D
PTS: 1
DIF:
1d266252-4683-11df-9c7d-001185f0d2ea
12-2 Arcs and Chords
DOK:
A
PTS: 1
DIF:
1d242706-4683-11df-9c7d-001185f0d2ea
DOK 1
F
PTS: 1
DIF:
DOK 1
B
PTS: 1
DIF:
1d1f3b3e-4683-11df-9c7d-001185f0d2ea
12-2 Arcs and Chords
DOK:
6. ANS:
REF:
TOP:
7. ANS:
REF:
TOP:
8. ANS:
REF:
DOK:
E
PTS: 1
DIF:
1d09ed12-4683-11df-9c7d-001185f0d2ea
12-1 Lines That Intersect Circles
DOK:
D
PTS: 1
DIF:
1d0eb1ca-4683-11df-9c7d-001185f0d2ea
12-1 Lines That Intersect Circles
DOK:
G
PTS: 1
DIF:
1d10ed16-4683-11df-9c7d-001185f0d2ea
DOK 1
1
TOP: 12-3 Sector Area and Arc Length
1
LOC: MTH.C.11.03.05.03.03.001
DOK 1
1
TOP: 12-2 Arcs and Chords
1
1
LOC: MTH.C.11.03.05.03.001
DOK 1
1
LOC: MTH.C.11.03.05.05.001
DOK 1
1
LOC: MTH.C.11.03.05.06.001
DOK 1
1
9. ANS: E
PTS: 1
DIF: 1
REF: 1d2febc2-4683-11df-9c7d-001185f0d2ea
TOP: 12-3 Sector Area and Arc Length
DOK: DOK 1
10. ANS: E
PTS: 1
DIF: 1
REF: 1d1a7686-4683-11df-9c7d-001185f0d2ea
TOP: 12-2 Arcs and Chords
DOK: DOK 1
1
TOP: 12-2 Arcs and Chords
TOP: 12-1 Lines That Intersect Circles
LOC: MTH.C.11.03.05.07.001
LOC: MTH.C.11.03.05.09.01.001
ID: A
MULTIPLE CHOICE
1. ANS: A
Step 1 Draw radius AD .
AD  10
AD  AF
Step 2 Use the Pythagorean Theorem.
Pythagorean Theorem
( AD ) 2  ( AC ) 2  ( CD ) 2
2
Substitute 10 for AD and 6 for AC.
(10) 2  (6) 2  ( CD )
( CD ) 2  64
CD  8
Subtract (6) 2 from both sides.
Take the square root of both sides.
Step 3 Find BD .
BD  2(8)  16
AF  BD , AF bisects BD .
Feedback
Correct!
Multiply this answer by 2.
Use the Pythagorean Theorem with a hypotenuse of length 10 and one leg of length 6 to
find the length of CD.
Use the Pythagorean Theorem with a hypotenuse of length 10 and one leg of length 6 to
find the length of CD.
A
B
C
D
PTS:
OBJ:
LOC:
KEY:
2. ANS:
1
DIF: 2
REF:
12-2.4 Using Radii and Chords
STA:
MTH.C.11.03.05.04.004
TOP:
circle | radius | chord
DOK:
A
Ê m ˜ˆ˜
˜˜
L  2r ÁÁÁÁ 360
Formula for arc length
¯
Ë
ˆ˜˜
Ê
˜˜
 2(2) ÁÁÁÁ 130
Substitute.
360
¯
Ë

13
9
 in  4.5 in
1cd7db86-4683-11df-9c7d-001185f0d2ea
MCC9-12.G.SRT.8
12-2 Arcs and Chords
DOK 2
Simplify.
Feedback
A
B
C
D
Correct!
Use the formula for finding the distance along an arc.
The arc length is equal to 2 times pi times the radius times the measure of the arc
divided by 360 degrees.
Use the formula for finding the distance along an arc.
PTS:
OBJ:
LOC:
KEY:
1
DIF: 2
12-3.4 Finding Arc Length
MTH.C.12.11.02.006
arc length
DOK: DOK 2
REF: 1cdedb8a-4683-11df-9c7d-001185f0d2ea
STA: MCC9-12.G.C.5
TOP: 12-3 Sector Area and Arc Length
2
ID: A
3. ANS: A
mWX  mYZ
3x  2  4x  3
2 x3
5x
mWX  3(5)  2  17
Congruent chords have congruent arcs.
Substitute the given measures.
Subtract 3x from both sides.
Add 3 to both sides.
Substitute 5 for x and simplify.
Feedback
A
B
C
D
Correct!
This is x. Now solve for the arc length.
Set the two expressions equal to each other and solve.
Congruent chords have congruent arcs.
PTS:
OBJ:
LOC:
KEY:
4. ANS:
1
DIF: 2
REF: 1cd7b476-4683-11df-9c7d-001185f0d2ea
12-2.3 Applying Congruent Angles, Arcs, and Chords
STA: MCC9-12.A.CED.1
MTH.C.11.03.05.03.02.006 | MTH.C.11.03.05.04.005
TOP: 12-2 Arcs and Chords
chord | arc measure
DOK: DOK 2
C
Feedback
A
B
C
D
One radian corresponds to 180 degrees.
One radian corresponds to 180 degrees.
Correct!
One radian corresponds to 180 degrees.
PTS: 1
DIF: 2
REF: 9167f1fb-6ab2-11e0-9c90-001185f0d2ea
OBJ: 12-3-Ext.1 Converting Degrees to Radians
STA: MCC9-12.G.C.5
TOP: 12-3-Ext Measuring Angles in Radians
KEY: convert | degrees | radians
DOK: DOK 2
5. ANS: A
A tangent is a line in the same plane as a circle that intersects it at exactly one point.
The point of tangency is the point where the tangent and a circle intersect.
The point of tangency on ñA or ñC is B(3, 0) . The tangent line is vertical and passes through point B(3, 0) .
Its equation is x  3.
Feedback
A
B
C
D
Correct!
The tangent line is a line in the same plane as a circle that intersects it at exactly one
point.
Find the point where the tangent and a circle intersect.
Find the point where the tangent and a circle intersect.
PTS:
OBJ:
LOC:
KEY:
1
DIF: 2
REF: 1cce2b06-4683-11df-9c7d-001185f0d2ea
12-1.2 Identifying Tangents of Circles
STA: MCC9-12.G.C.4
MTH.C.11.03.05.05.002 | MTH.C.11.03.05.05.003
TOP: 12-1 Lines That Intersect Circles
point of tangency | circles
DOK: DOK 2
3
ID: A
6. ANS: A
Ê m ˆ˜˜
˜˜
A  r 2 ÁÁÁÁ 360
¯
Ë
ÊÁ 54 ˜ˆ˜
2Á
= (4) ÁÁ 360 ˜˜
¯
Ë
2
= 2.4 cm
Formula for area of a sector
Substitute 4 for r and 54 for m.
Simplify.
Feedback
A
B
C
D
Correct!
Square the radius.
Divide by 360 degrees.
Use the formula for finding the area of a sector.
PTS:
OBJ:
LOC:
KEY:
7. ANS:
1
DIF: 1
REF: 1cda16d2-4683-11df-9c7d-001185f0d2ea
12-3.1 Finding the Area of a Sector
STA: MCC9-12.G.C.5
MTH.C.12.12.02.010
TOP: 12-3 Sector Area and Arc Length
circle | sector area
DOK: DOK 2
B
Feedback
A
B
C
D
How many revolutions are there in one revolution?
Correct!
How many revolutions are there in one revolution?
How many revolutions are there in one revolution?
PTS: 1
DIF: 3
REF: 916a5456-6ab2-11e0-9c90-001185f0d2ea
STA: MCC9-12.G.C.5
TOP: 12-3-Ext Measuring Angles in Radians
KEY: revolutions per minute | angular speed | radians
DOK: DOK 3
4
ID: A
8. ANS: A
Ê m ˆ˜˜
˜˜
A  r 2 ÁÁÁÁ 360
¯
Ë
ÊÁ 120 ˜ˆ˜
2Á
 (30) ÁÁ 360 ˜˜
¯
Ë
 300 cm 2
Formula for area of a sector
Substitute the given values.
Simplify.
Feedback
A
B
C
D
Correct!
Use the formula for finding the area of a sector.
Use the formula for finding the area of a sector.
The area of a sector is equal to pi times radius squared times the measure of the arc
divided by 360 degrees.
PTS:
OBJ:
LOC:
KEY:
9. ANS:
1
DIF: 2
12-3.2 Application
MTH.C.12.12.02.010
circle | sector area
B
REF:
STA:
TOP:
DOK:
1cdc792e-4683-11df-9c7d-001185f0d2ea
MCC9-12.G.C.5
12-3 Sector Area and Arc Length
DOK 2
Feedback
A
B
C
D
One radian corresponds to 180 degrees.
Correct!
One radian corresponds to 180 degrees.
One radian corresponds to 180 degrees.
PTS:
OBJ:
TOP:
DOK:
1
DIF: 1
REF: 9168190b-6ab2-11e0-9c90-001185f0d2ea
12-3-Ext.2 Converting Radians to Degrees
STA: MCC9-12.G.C.5
12-3-Ext Measuring Angles in Radians
KEY: convert | degrees | radians
DOK 2
5
Module 12 Practice Quiz [Answer Strip]
C
_____
4.
ID: A
B
_____
7.
A
_____
1.
A
_____
5.
A
_____
8.
E
_____
1.
D
_____
2.
B
_____
9.
A
_____
3.
F
_____
4.
B
_____
5.
A
_____
2.
E
_____
6.
D
_____
7.
A
_____
6.
G
_____
8.
A
_____
3.
E
_____
9.
E 10.
_____