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Geometry Exam Review: Sample question from CH 7-11. CH 12 not included as we just tested on
it.
Multiple Choice
Identib) the choice that best completes the statement or answers the question.
•
6 Find the circumference of the circle. Use 7z- = 3.14.
1 The expressions (3x + 16) and (6x — 40) ° represent
two angle measures of a regular polygon. Find the
measure of an angle of the polygon.
CD 120°
® 108°
0 72°
® 30°
2 Name a polygon with 6 sides.
CD 226.08 in.
® 29.72 in.
C) 1017.36 in.
® 113.04 in.
7 A scuba diver has a taut rope connecting the dive
boat to an anchor on the ocean floor. The rope is 85
feet long. The water is 45 feet deep. To the nearest
tenth of a foot, how far is the anchor from a point
directly below the boat?
0 72.1 ft
® 77.6 ft
C) 60.1 ft
® 96.2 ft
8 How long is a string reaching from the top of a 17-ft
pole to a point on the ground that is 5 ft from the
base of the pole?
CD octagon
® quadrilateral
0 pentagon
® hexagon
3 The area of a triangle is 4,000 sq. m, and it's height
is 50m. What is length of the base?
CD 160m
® 80m
C) 120m
® 100 m
4 The area of a circle is 1,017.36 sq. in. What is the
circumference of the circle? (use the 7z- = 3.14)
CD 128.8 in.
® 113.04 in.
C) 18 in.
® 24 in.
5 A wooden fence is to be built around a 26 m-by-72
m lot. How many meters of fencing will be needed?
O
4314 ft
®
4324 ft
0 4264 ft
® 4274 ft
9 Which set of lengths cannot form a right triangle?
CD 516m
® 1032m
C) 196m
® 194m
CD
®
C)
®
1
10 mm, 24 mm, 26 mm
20 mm, 48 mm, 52 mm
5 mm, 12 mm, 13 mm
11 mm, 24 mm, 26 mm
Find the value of x. (The figure may not be drawn to
scale.)
10 The longer leg of a 30°-60°-90° triangle is 7.6 feet
long. Find the perimeter.
® 35.96 ft
® 8.77 ft
() 20.77 ft
® 25.77 ft
11 Liola drives 12 km up a hill that is at a grade of 13 ° .
What horizontal distance, to the nearest tenth of
kilometer, has she covered?
® 12.7 km
® 11.7 km
() 2.7 km
® 2.8 km
15
12 Find the number of sides of a convex polygon if the
measures of its interior angles have a sum of 2340°.
® 121
® 46
® 44
® 61
16 Find the area of the parallelogram.
® 13
® 14
® 15
® 17
13 Assume that ZA is an acute angle and has a sin
value of 0.994. What is the measure of ZA to two
decimal places?
/ 4.5 cm
® 0.02°
® 83.72°
C) 89.98°
® 44.83°
1.6 cm
14 Find the missing angle and side measures of AABC ,
given that mZA = 20°, mZC = 90°, and CB = 20.
®
®
C)
®
® 11 cm2
® 11.04 cm2
C) 5.04 cm2
® 10.07 cm2
mZB = 110°, c = 58.5, b = 55.4
mZB = 70°, c = 59, b = 54.9
mZB = 70°, c = 58.5, b = 54.9
mZB = 110°, c = 58.5, b = 54.9
2
21 A slide 2.5 m long makes an angle of 26° with the
ground. How high is the top of the slide above the
ground?
17 A radio station is going to construct a 12-foot tower
on top of a building. The tower will be supported by
three cables, each attached to the top of the tower
and to points on the roof of the building that are 16
feet from the base of the tower. Find the total length
of the three cables.
CD 2.25m
® 1.13m
C) 1.22m
® 1.1 m
22 Which choice represents the trigonometric ratio: cos
CD 60 ft
® 80 ft
C) 20 ft
® 100 ft
18 Which set of lengths cannot form a right triangle?
CD 16 mm, 30 mm, 34 mm
® 4 mm, 7.5 mm, 8.5 mm
() 8 mm, 15 mm, 17 mm
® 9 mm, 15 mm, 17 mm
19 The shorter leg of a 30°-60°-90° triangle is 7.6 feet
long. Find the perimeter.
CD 13.16 ft
® 15.2 ft
C) 35.96 ft
® 22.8 ft
20 A photographer shines a camera light at a particular
painting forming an angle of 44° with the camera
platform. If the light is 56 feet from the wall where
the painting hangs, how high above the platform is
the painting?
23 What is x to the nearest hundredth? (not drawn to
scale)
18
X
•
CD x=14.58
• x = 13.99
C) x=11.33
• x = 22.23
53ft
CD 0.97 ft
® 54.08 ft
C) 57.99 ft
® 1.04 ft
3
390
24 Write cos B.
27 Identify two chords.
3
A
/7\
vaa
4
B
4
5
3
4
3
0
®
C)
®
5
Nu,
4
3
25 Solve for x to the nearest degree.
RS and TU
RT and SU
TU and VW
RS and VW
28 A line which intersects a circle at exactly one point
is called
.
CD a point of tangency
® a tangent line
C) a chord
® a secant
29 (Imagine or make a sketch to help you answer). SR
is tangent to OQ at R. Choose the true statement.
CD 72
® 71
© 18
® 19
CD mZRQS + mZQSR = 180°
•
mZRQS= 90°
0 mZSRQ = 90°
26 Find the missing angle and side measures of AABC,
given that mZA = 50°, mZC = 90°, and CB = 16.
CD
®
C)
®
•
SQ SR
30 The circle is circumscribed by the pentagon as
shown (not drawn to scale). If QZ = 12, YX = 8,
XW= 9, UW= 18, and SU= 15, find the perimeter
of the pentagon.
mZB = 40°, c = 20.4, b = 13.4
mZB = 140°, c = 20.9, b = 13.9
mZB = 40°, c = 20.9, b = 13.4
mZB = 140°, c = 20.9, b = 13.4
CD 124
® 129
® 88
® 93
4
31 You are standing at point B. Point B is 11 feet from
33 How many degrees does a minute hand move in 10
minutes?
the center of the circular water storage tank and 10
feet from point A. AB is tangent to 00 at A. Find
the radius of the tank.
A
11
12
1
10
10
2
® 80°
® 60°
C) 40°
® 50°
34 A wooden wagon wheel has 12 equally spaced
spokes radiating from the central hub.
® 9.2 ft.
® 11.1 ft.
C) 4.6 ft.
® 14.9 ft.
32 Given: In 00, mBAC = 316°. Find mZBOC.
•
•
%
What is the measure of the angle that determines the
separation between two adjacent spoke holes?
®
®
C)
®
® 19°
® 38 0
C) 44°
® 22°
5
22.5°
30°
12°
45°
35
Use the diagram (not drawn to scale) and the given
information.
Find the value of x.
118°, mDEF = 90°, mFGH = 140°, and
mHAB = 12°
Find m/FPD.
37 mBCD =
® 14.4
® 11.9
0 17.5
® 10.6
36 Given: m/IED = 99° and m Z.IFG = 92°
Find the measure of each unknown angle. (not
drawn to scale)
®
®
0
®
38
®
®
0
®
12°
25°
106°
39 0
A park maintenance person stands 24 m from a
circular monument. If you draw two tangents from
the maintenance person to each side of the
monument, they make an angle of 22°. What is the
measure of the arc created where the lines intersect
the monument (the arc closest to the person)?
® 68°
® 112°
0 136°
® 158°
mZ1 = 81°, mZ2= 88°, mZ3 = 92°, mZ4= 99°
mZ1 = 88°, mZ2= 81°, mZ3= 99°, mZ4= 92°
mZ1 = 88°, mZ2= 81°, mZ3= 92°, mZ4= 99°
mZ1 = 81°, mZ2= 88°, mZ3= 99°, mZ4= 92°
6
Use the diagram (not draw to scale) and the given
information.
Use the diagram (not drawn to scale) and the given
information to find the diameter of the circle. Round
your answer to the nearest tenth.
A
A
41 BC = 18 and DC = 22.
39 Find the value of x if mAB = 59° and mCD = 71°
® 44.9
® 7.3
® 8.9
® 6.2
42 A footbridge is in the shape of an arc of a circle.
The bridge is 11 ft tall and 26 ft long, horizontally.
What is the radius of the circle that contains the
bridge? Round your answer to the nearest tenth.
® 6°
® 65°
0 32.5°
® 67°
40 A hummingbird is flying toward a large tree that has
a radius of 6 feet. When it is 35 feet from the center
of the tree, its lines of sight form two tangents. What
is the measure of the arc on the tree that the
hummingbird can see?
r
® 13.2 ft
® 2.2 ft
0 15.4 ft
® 26.4 ft
16 ft
Find the value of x.
®
®
0
®
161.26°
160.26°
81.13°
80.13°
43
®
®
0
®
7
12
28
6
14
44
48 The area of a regular octagon is 30 cm 2 . What is the
area of a regular octagon with sides five times as
large as the sides of the first octagon?
® 685 cm2
® 4500 cm2
C) 150 cm2
® 750 cm2
49 Leila needs to make a poster that is 2 m by 3.5 m for
the big game. The cost of the paper is $2.75. Later
she needs another poster with dimensions 1 m by
1.75 m. What is the paper for this poster likely to
cost?
® $0.44
® $0.69
C) $1.38
® $1.63
50 Find the area of an equilateral triangle with side
length 8.
• 16.\5
• 12.\5
© 32
® 24
51 Find the area of a regular octagon with side length 9
cm.
O 782.2 cm2
® 423.3 cm2
C) 374.4 cm2
® 391.1 cm2
52 If a circle has a diameter of 5 inches, what is the
circumference rounded to the nearest whole number?
Use 7Z" 3.14.
® 8 in.
® 20 in.
C) 32 in.
® 16 in.
53 A circle has a circumference of 35 meters. Find its
radius.
® 8.75m
® 5.57m
C) 17.5 m
® 11.14m
16
O 8
® none of these
0 2
® 3
45 The figure below is made up of two squares with the
areas shown. What is the length of x?
® 850
® 100
C) 160
® 3400
46 A rectangular field is 340 m by 450 m. A
rectangular barn 22 m by 45 m is built in the field.
How much area is left over?
O 153, 990 m2
® 151, 997 m2
C) 152, 010 m2
® 152, 933 m2
47 The area of a trapezoid is 230 in 2 . If the height is 10
in. and the longer base is 33 in., what is the length of
the shorter base? Round your answer to the nearest
tenth.
® 23.0 in.
® 13.0 in.
C) 10.0 in.
® 7.0 in.
8
54 A park has a circular swimming pool. The diameter
of the pool is 11 m. What is the distance traveled if
you swim around the edge of the pool once?
Use 7Z" ,- 3.14.
® 34.54m
® 103.67m
0 22m
® 69.12m
57 The change in position from the solid figure to the
dotted figure is best described as a
Find the area, use Pi =3.14:
® transmission
® reflection
0 rotation
® translation
58 A point P has coordinates (1, –3). What are its new
coordinates after point P is reflected over the y-axis?
® (-1, –3)
® (1, –3)
0 (1,3)
® (-1, 3)
59 What is the translation image of (5, 6) after the
translation (x, y) —> (x– 3,y– 1)?
0 (8,5)
® (2,7)
® (8,7)
® (2,5)
60 Identify the coordinates of the point (-7, 6) after a
rotation of 90° clockwise about the origin.
® (7,6)
® (-7, –6)
0 (6,7)
® (7, –6)
55
® 20.096m
® 8.0384m
0 32.1536m
® 128.614m
56 Find the area of the shaded region.
30.79 cm2
38.48 cm2
153.94 cm2
123.15 cm2
9
61 One triangle is shown on the coordinate grid. Two
vertices for a second triangle are also shown. Which
coordinates for the third vertex will form another
triangle that is similar to the triangle that is shown?
63 A reflection is always
® a rotation
® a translation
() an isometry
® reflexive
64 Use the graph below to complete the sentence.
1F1 x
jee"lp x
B
**•
—10 —
62
®
(-5, —2)
®
( -5 , —9)
©
( -5 , —7 )
®
( -5 , 7 )
A
—10
Figure A i 13' C i D i is the image of figure ABCD under
a rotation
® 180° about the origin.
® 270° counterclockwise about the origin.
C) 90° clockwise about the origin.
® 90° counterclockwise about the origin.
65 Which of the following letters (if drawn as simply as
possible) has at least one line of symmetry?
Y, N, P, R
CD R
• Y
• P
® N
What are the coordinates of the vertices when the
figure is reflected in line m?
10
—ict
'PPP-
10
—10
W' (4, —3), X' (1, 4), /7 ' (-2, 0)
® W' (-3, 4), X' (4, 1), /7 ' (0, —2)
0 W' (2, 3), X' (-1, —4), /7 ' (-4, 0)
W' (2, —3), X' (1, —4), /7 ' (-4, 0)
10