Name: _________________________________________
Date: _____________________
DATE/TIME of my exam: ____________________________________
TO THE STUDENT: While these review materials will cover the basic material of the course, and are
designed to prepare you for the final exam, they are NOT all inclusive. The final exam will consist of 3
sections.
1) Multiple Choice – NON CALCULATOR (15 questions, 1 point)
2) Multiple Choice – CALCULATOR (25 questions – 1 point)
3) Free Response – CALCULATOR (choose 5 of 7 questions, 8 point)
Teacher:
BUONO
KURTZMAN KATUNDU
MOSKOVITZ
VIESTO/PULCINI
Circumference of a circle: C   d  2 r
Arc Length of a Sector: = C
m central 
360o
AREA
circle
A = π r2
parallelogram
A = bh
rectangle
A = bh or A = l w
regular polygon
A=
rhombus
A = 12 d1d 2
sector of a circle
A=
square
A = s2
trapezoid
A=
triangle
A = 12 bh
1
2
Pa
m central 
360o
1
2
 r2
b1  b2  h
SURFACE AREA OF A SOLID
Lateral Surface Area
1
2
Pl
regular pyramid
L=
right circular cone
L = r l
right cylinder
L = 2 rh
right prism
L = Ph
Total Surface Area
1
2
Pl + B
regular pyramid
T=
right circular cone
T =  r l + π r2
right cylinder
T = 2 rh + 2π r2
right prism
T = Ph + 2B
sphere
T = 4πr2
VOLUME
cube
V  s3
right circular cone
V  13 Bh
right cylinder
V   r 2h
right prism
V  Bh
right pyramid
V  13 Bh
sphere
V  43  r 3
Final Exam Review packet Geometry A
2014
Chapter 7. 5 Apply The Tangent Ratio
1. Find the height of the lamppost to the nearest inch.
2. You stand 40 feet from the base of a tree. You measure the angle of elevation from a point on
the ground to the top of the tree to be 66°. Find the height of the tree to the nearest foot.
3. The angle of elevation from the base to the top of a water slide is about 17°. The horizontal
distance from the top of the waterslide to the bottom of the waterslide is about 150 feet. Find
the height h of the waterslide to the nearest foot.
Final Exam Review packet Geometry A
2014
4. To determine how tall is the screen of a drive-in movie, to the nearest foot, a student writes the
solution below.
Your job is to describe the mistake in complete sentences and to use accurate math and viable
arguments to correct the answer.
Cos (58°) = x/50
50 cos (58°) = x
X ̴ 5.959 ft.
X ̴ 6ft
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
5. You are a block away from a skyscraper that is 780 feet tall. Your friend is between the
skyscraper and yourself. The angle of elevation from your position to the top of the skyscraper is
42°. The angle of elevation from your friend’s position to the top of the skyscraper is 71°. To the
nearest foot, how far are you from your friend?
Final Exam Review packet Geometry A
2014
Chapter 7.6 Apply Sine and Cosine Ratios
1.) Find the length of the missing side.
A.) 6.3
B.) 11.7
C.) 16.2
D.) 16.8
E.) 30.9
2.) Find the length of the missing side.
A.) 4.9
B.) 6.4
C.) 7.2
D.) 7.4
E.) 52.3
3.) Find the length of the missing side.
A.) 7.9
B.) 41.1
C.) 54.1
D.) 55.9
E.) 57.2
4.) Find the length of the missing side.
A.) 8.9
B.) 23.7
C.) 29.8
D.) 40.3
E.) 40.5
5.) Find the length of the missing side.
A.) 12.0
B.) 12.8
C.) 14.5
D.) 30.2
E.) 30.5
Final Exam Review packet Geometry A
2014
1.) A rope, staked 20 feet from the base of a building, goes to the roof and forms an angle of
58o with the ground. Sketch a drawing to represent the information. To the nearest tenth of a
foot, how long is the rope?
2.) Michael is standing 80 feet from the base of a cliff. He looks up and measures the angle of
elevation to be 56o. To the nearest foot, find the height of the cliff.
3.) A pilot is looking at an airport from his plane. He measures the angle of depression to be
29o. If the plane is at an altitude of 10,000 feet, approximately how far, to the nearest tenth, is
it from the plane to the airport?
4.) A brown colored barking dog is looking up at a grey colored squeaking squirrel at the top of
a weeping willow tree. The distance between the two animals is 55 feet, and the dog uses his
handy-dandy protractor to measure the angle of elevation to the squirrel as 64 degrees. (a)
How high is the grey squeaking squirrel above the ground? (b) How far is the brown barking
dog from the base of the weeping willow tree?
5.) Bill and Jeff went to visit the Statue of Liberty. They read in the tourism guidebook the
height of the Statue of Liberty is 151 ft. from the base to the torch. Bill is standing on one side
of the Statue of Liberty and measures the angle of elevation to the top of the torch to be 37 o.
Jeff is standing on the opposite side of the Statue of Liberty and measures the angle of
elevation to the top of the torch to 56o. To the nearest foot, how far apart are Bill and Jeff from
each other?
Final Exam Review packet Geometry A
2014
Chapter. 7.7 Solve Right Triangles
1.) Find the measure of the indicated angle to the nearest degree.
A.)
B.)
C.)
D.)
E.)
16°
18°
20°
22°
24°
2.) Find the measure of the indicated angle to the nearest degree.
A.) 26°
B.) 32°
C.) 36°
D. ) 42°
E.) 46°
3.) Find the missing side. Round your answer to the nearest tenth.
A.)
B.)
C.)
D.)
E.)
15.5
16.6
20.5
24.3
27.8
4.) Find the missing side. Round your answer to the nearest tenth.
A.)
B.)
C.)
D.)
E.)
17.9
15.5
12.4
11.2
8.0
5.) Find the missing side. Round your answer to the nearest tenth.
A.)
B.)
C.)
D.)
E.)
11.3
14.2
15.0
16.2
18.3
Final Exam Review packet Geometry A
2014
Chapter 8: Quadrilaterals
1.) In rectangle JKLM, solve for the value of X and Y.
A.) x  12, y  9
B.) x  10, y  15
C.) x  7, y  5
D.) x  2, y  10
E.) x  4, y  12
2.) Critique the work of the student shown in the example below. Describe the mistake in complete
sentences and using accurate math computations correct the answer.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
3.) Find the measure of one of the missing interior angles of the polygon.
A.) 1030
B.) 270 0
C.) 3730
D.) 5400
E.) 9000
Final Exam Review packet Geometry A
2014
4.) The floor of greenhouse show is shaped like a regular decagon. Find the measure of an interior
and exterior angle respectively.
A.) 14400 ,3600
B.) 1800 , 720
C.) 1440 ,360
D.) 1200 ,180
E.) 1080 , 450
5.) JKLM is a parallelogram. Solve for the m LMK .
A.) 1100
B.) 550
C.) 40 0
D.) 300
E.) 600
6.) The mirror shown is attached to the wall by an arm that can extend away from the wall. In the
figure Points P, Q, R, and S are the vertices of a parallelogram. This parallelogram is one of
several that change shape as the mirror is extended. Create a viable argument to explain what
happens to m P as Q increases?
Final Exam Review packet Geometry A
2014
7.) QRST is a rectangle. Given that QS  12 and diagonals that intersect at point P, solve for RS.
A.)
B.)
C.)
D.)
E.)
6.71
6.35
9.95
21.46
8.09
8.) LMNP is a square. Given that LK = 1, find the perimeter of LMNP.
A.)
B.)
C.)
D.)
E.)
1.41
4.00
5.65
6.93
8.00
9.) Classify the quadrilateral given the vertices.
A.)
B.)
C.)
D.)
E.)
Parallelogram
Rectangle
Square
Trapezoid
Rhombus
10.) Find the sum of the measures of the interiors angles of a convex 22-gon.
A.) 39600
B.) 36000
C.) 4320 0
D.) 72000
E.) 79200
Final Exam Review packet Geometry A
2014
11.) You want to mark off a square region in your yard for a patio. You use a tape measure to mark
off a quadrilateral on the ground. Each side of the quadrilateral is 2.5 meters long. Create a
viable argument explaining how you can use the tape measure to make sure that the
quadrilateral you drew is a square.
12.) Solve for the measure of MN in the given trapezoid.
A.)
B.)
C.)
D.)
E.)
46
23
20
19
15
13.) In trapezoid PQRS, PQ RS and MN is the midsegment of PQRS. If RS  5* PQ , what is
the ratio of MN to RS?
A.)
B.)
C.)
D.)
E.)
3:5
5:3
2:1
3:1
3:2
14.) The measure of one interior angle of a parallelogram is 50 degrees more than 4 times the
measure of another angle. Find the measure of the largest angle.
A.) 26 0
B.) 620
C.) 1540
D.) 2980
E.) 3100
Final Exam Review packet Geometry A
2014
15.) If each interior angle of a regular n-gon has a measure of 1560 , find the number of sides the
polygon has.
A.)
B.)
C.)
D.)
E.)
13
14
15
24
31
16.) Solve for X.
A.)
B.)
C.)
D.)
E.)
1.167
3
5
10
25
17.) Find the perimeter of the given rectangle.
A.)
B.)
C.)
D.)
E.)
28
45
81
103
149
18.) The diagonals of a rhombus are 10 centimeters and 24 centimeters. Find the perimeter of the
rhombus. Correct the work of the student below and use complete sentences to explain correct
work.
Final Exam Review packet Geometry A
2014
19.) Solve for n and m in the given parallelogram.
A.) n  9, m  4
B.) n  4.5, m  2
C.) n  11, m  4
D.) n  3, m  4
E.) n  9, m  20
20.) Give the most specific classification of ABCD using the given information on the figure.
A.)
B.)
C.)
D.)
E.)
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
21.) Find the m M .
A.) 1210
B.) 1180
C.) 620
D.) 590
E.) 310
22.) In
PQRS , PS  5cms, QP  10cms, and m PQR  360 . Sketch a picture of PQRS. Label all
the side lengths and interior angle measures.
23.) Find the measure of one exterior angle measure of an octagon.
A.) 22.50
B.) 450
Final Exam Review packet Geometry A
C.) 300
D.) 600
E.) 1800
2014
Chapter 5: Relationships within Triangles
1.) In a triangle, a segment connecting the midpoints of two sides of the triangle is a called a _____.
A.)
B.)
C.)
D.)
E.)
Median
Altitude
Centroid
Midsegment
Incenter
5
̅̅̅̅ and D is the
2.) Solve for x given 𝐵𝐷 = 2 𝑥 + 4 and 𝐴𝐸 = 6𝑥 + 4. Assume B is the midpoint of 𝐴𝐶
midpoint of ̅̅̅̅
𝐶𝐸 .
1
A.) − 2
B.) 4
C.) 2
D.) −
1
4
E.) −2
3.) For the triangle shown, VS = 5 and VQ = 6. Then PQ = ________.
A.)
B.)
C.)
D.)
E.)
11
12
10
5
6
⃡ , then ∠𝐾𝐺𝐹 ≅ _______________________.
⃡ is the perpendicular bisector of 𝐺𝐻
4.) If 𝐾𝐹
A.)
B.)
C.)
D.)
E.)
∠𝐹𝐾𝐺
∠𝐾𝐹𝐻
∠𝐾𝐹𝐺
∠𝐹𝐾𝐻
∠𝐾𝐻𝐹
Final Exam Review packet Geometry A
2014
5.) In the diagram, X is the incenter of Δ𝑅𝑇𝑉. Find XU.
A.)
B.)
C.)
D.)
E.)
12
13
5
6.5
6
6.) Find the value of x.
A.)
B.)
C.)
D.)
E.)
10
-10
9
11
-9
7.) Find the value of x.
A.)
B.)
C.)
D.)
E.)
10
11
12
13
14
8.) Find the longest segment in the figure.
A.)
B.)
C.)
D.)
E.)
̅̅̅̅
𝐿𝑁
̅̅̅̅
𝑁𝑃
̅̅̅̅̅
𝑃𝑀
̅̅̅̅
𝑀𝐿
̅̅̅̅̅
𝑀𝑁
Final Exam Review packet Geometry A
2014
9.) Which side lengths allow you to construct a triangle?
A.)
B.)
C.)
D.)
E.)
2, 3, 8
4, 1, 9
7, 2, 2
6, 8, 10
5, 3, 2
10.) Two sides of a triangle have lengths 7 and 13. The third side has a length that is _________.
A.)
B.)
C.)
D.)
E.)
Greater than 13 and less than 20
Greater than 6 and less than 13
Less than 20 and greater than 6
Greater than 20
Less than 6
11.) In the figure, V is the centroid of Δ𝑅𝑆𝑇. Find 𝑉𝑈.
A.)
B.)
C.)
D.)
E.)
6.25
10
5
2.5
7.5
12.) The perpendicular bisectors of Δ𝐴𝐵𝐶 meet at point D. Find BD.
A.)
B.)
C.)
D.)
E.)
6
12
18
21
10.5
Final Exam Review packet Geometry A
2014
13.) The town of Greenwich is holding elections. The town sets up three polling stations around the
area that form a triangle. They decide to meet at the circumcenter of their locations. The
circumcenter is equidistant from the three ___________________________ of the triangle
formed by the polling stations.
A.)
B.)
C.)
D.)
E.)
Vertices
Angles
Angle bisectors
Sides
Midsegments
14.) For the triangle, find the coordinates of the point of concurrency of the altitudes.
A.)
B.)
C.)
D.)
E.)
(2, −3)
(−4, −3)
(−4, 1)
(−1, −1)
(−1, −3)
15.) Refer to the figure. Given ̅̅̅̅
𝐴𝐹 ≅ ̅̅̅̅
𝐹𝐶 and ∠𝐴𝐵𝐸 ≅ ∠𝐸𝐵𝐶, the median of Δ𝐴𝐵𝐶 is ___________.
A.)
B.)
C.)
D.)
⃡𝐺𝐹
̅̅̅̅
𝐵𝐷
̅̅̅̅
𝐴𝐹
̅̅̅̅
𝐵𝐹
E.) ⃡𝐵𝐸
16.) In the diagram at the right, P is the centroid of Δ𝐴𝐶𝐷.
a) MC = ____________________
b) AP = ____________________
Final Exam Review packet Geometry A
2014
17.) 𝐴𝐵 is the perpendicular bisector of ̅̅̅̅
𝐶𝐷. 𝐴𝐵 bisects ∠𝐶𝐴𝐷.
a) Find the value of x.
b) Find the value of y.
18.) In the diagram shown, the perpendicular bisectors of Δ𝑋𝑌𝑍 meet at point O.
a) If 𝑍𝑂 = 6, find YO.
b) What is point O called?
19.) You can balance a triangle-shaped object by finding the centroid of the triangle. The length of
one median is 21 centimeters.
a) How far from the vertex of the angle that the median was drawn is the centroid?
b) Construct a viable argument as to why this point is the best point to choose to balance the
object.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
____________________________________________________________________________________
Final Exam Review packet Geometry A
2014
Chapter 10: Properties of Circles
1.) Find mHEG .
A.) 58o
B.) 115o
C.) 140o
D.) 235o
E.) 285o
2.) Find mIJ .
A.) 60o
B.) 61o
C.) 69o
D.) 70o
E.) 89o
3.) Find mBC .
A.) 82o
B.) 119o
C.) 129o
D.) 130o
E.) 180o
4.) Find mBCZ .
A.) 84o
B.) 90o
C.) 92o
D.) 115o
E.) 210o
Final Exam Review packet Geometry A
2014
5.) Find mLM .
A.) 68o
B.) 110o
C.) 118o
D.) 120o
E.) 138o
6.) Find mEGF .
A.) 26o
B.) 40o
C.) 45o
D.) 59o
E.) 65o
7.) Find the measure of SU .
A.) 131o
B.) 134o
C.) 153o
D.) 157o
E.) 169o
8.) Find the measure of the indicated arc.
A.) 200o
B.) 214o
C.) 240o
D.) 253o
E.) 274o
Final Exam Review packet Geometry A
2014
9.) Find the measure of the indicated arc.
A.) 135o
B.) 200o
C.) 205o
D.) 220o
E.) 250o
10.) Find mML .
A.) 150o
B.) 155o
C.) 226o
D.) 246o
E.) 254o
11.) Find the measure of the indicated arc.
A.) 208o
B.) 218o
C.) 231o
D.) 238o
E.) 242o
12.) Find the perimeter of the circumscribed polygon.
A.) 48.1
B.) 63.2
C.) 75.9
D.) 78.6
E.) 84.6
Final Exam Review packet Geometry A
2014
13.) Identify the center and radius of the circle. Then sketch its graph.
14.) Write the equation of the circle with a radius of 4 and center at (-15 , -2).
A.) (x – 2)2 + (y + 15)2 = 16
B.) (x – 15)2 + (y – 2)2 = 16
C.) (x + 15)2 + (x + 2)2 = 4
D.) (x + 15)2 – (x + 2)2 = 1
E.) (x + 15)2 + (x + 2)2 = 16
15.) Write the equation of the circle whose diameter has endpoints at (-1 , 12) and (-7 , 2).
A.) (x + 4)2 + (y – 7)2 = 96
B.) (x – 4)2 + (y + 7)2 = 34
C.) (x + 4)2 + (Y – 7)2 = 34
D.) (x – 4)2 + (y – 7)2 = 34
E.) (x + 8)2 + (y – 6)2 = 34
Final Exam Review packet Geometry A
2014
16.) A quadrilateral garden is inscribed in a circular fence. Two if the angles in the garden
are 100o and 60o. Find the measure of the other two angles. Explain how you solved the
problem.
17.) Peter the Pizza Maker just finished
cooking the pizza to the right and his partner,
Paul, sliced the pizza. Paul ran the cutter
directly through the center of the pizza, and
then measured the central angles that he cut.
Before he could finish measuring, the
customer came to get their pizza. Find the
measures of the other four central angles, A,
B, C and D.
55o D
C
65o
A B
18.) A bicycle wheel, pictured, has 16 spokes, equally
spaced around the wheel. Find the measure of each
central angle.
Final Exam Review packet Geometry A
2014
19.) A frog is sitting 6 feet from a circular pool,
and 18 feet from a point of tangency to the pool.
18 feet
Find the radius of the pool.
6 feet
20.) The minute hand on a clock is 9 inches long and the hour hand is 5 inches long. What
arc measure does the minute hand sweep through in 20 minutes? In 45 minutes?
Chapter 11: Measuring Length and Area
1.) Find the missing side length.
A.)
B.)
C.)
D.)
E.)
28.1 ft.
56.5 ft.
84.3 ft.
102.1 ft.
121.3 ft.
2.) Find the missing side length.
A.) 43.7 km
B.) 45.3 km
C.) 47.3 km
D.) 55 km
E.) 55.3 km
Final Exam Review packet Geometry A
2014
3.) Find the area
A.)
B.)
C.)
D.)
E.)
7.6 sq. cm
10.6 sq. cm
15.2 sq. cm
30.4 sq. cm
34.2 sq. cm
4.) Find the area.
A.) 35.4 𝑦𝑑2
B.) 38.9 𝑦𝑑2
C.) 41.8 𝑦𝑑2
D.) 70.8 𝑦𝑑2
E.) 71.8 𝑦𝑑2
5.) Find the area
A.) 29.6 𝑚2
B.) 3.7 𝑚2
C.) 14.8 𝑚2
D.) 7.4 𝑚2
E.) 12.3 𝑚2
6.) Find the missing measurement. Round to the tenths place.
A.) 8.8 m
B.) 9.4 m
C.) 10.9 m
D.) 13 m
E.) 14.2 m
Final Exam Review packet Geometry A
2014
7.) The polygons are similar. Find the scale factor of the smaller figure to the larger figure.
A.)
B.)
C.)
D.)
E.)
1:2
2:1
5:6
6:5
7:8
8.) The polygons are similar. Find the scale factor of the smaller figure to the larger figure.
A.) 1:2
B.) 1:3
C.) 1:4
D.) 3:2
E.) 3:4
9.) Find the length of the arc. Round your answer to the nearest tenths.
A.) 31.4 𝑦𝑑
B.) 66.0 𝑦𝑑
C.) 395.8 𝑦𝑑
D.) 628.3 𝑦𝑑
E.) 712.2 𝑦𝑑
10.) Find the area of the sector.
A.)
169𝜋
3
𝑦𝑑2
B.) 8𝜋 𝑦𝑑2
13𝜋
3
27𝜋
D.) 4
C.)
𝑦𝑑2
𝑦𝑑2
E.) 64𝜋 𝑦𝑑2
Final Exam Review packet Geometry A
2014
11.) Find
A.) 104°
B.) 121°
C.) 261°
D.) 264°
E.) 293°
12.) Find
A.) 82°
B.) 105°
C.)126°
D.) 214°
E.) 243°
13.) Solve for x
A.) 5
B.) 6
C.) 7
D.) 8
E.) 9
14.) Solve for x
A.) 5
B.) 6
C.) 7
D.) 8
E.) 9
Final Exam Review packet Geometry A
2014
15.) Find the area of the sector.
A.) 8π 𝑚𝑖 2
B.) 20π 𝑚𝑖 2
C.) 40π 𝑚𝑖 2
D.) 64π 𝑚𝑖 2
E.) 72π 𝑚𝑖 2
16.) Find the area of the sector
A.)
B.)
C.)
D.)
E.)
44.2 𝑦𝑑2
444.2 𝑦𝑑2
538.8 𝑦𝑑2
583.8 𝑦𝑑2
853.3 𝑦𝑑2
17.) Find the area of the regular polygon. Round your answer to the nearest tenths place.
A.)
B.)
C.)
D.)
E.)
129.8 𝑠𝑞. 𝑢𝑛𝑖𝑡𝑠
332.4 𝑠𝑞. 𝑢𝑛𝑖𝑡𝑠
340.2 𝑠𝑞. 𝑢𝑛𝑖𝑡𝑠
1329.6 𝑠𝑞. 𝑢𝑛𝑖𝑡𝑠
1456.7 𝑠𝑞. 𝑢𝑛𝑖𝑡𝑠
18.) Find the area of the regular polygon.
A.) 166.3 𝑢𝑛𝑖𝑡𝑠 2
B.) 374.1 𝑢𝑛𝑖𝑡𝑠 2
C.) 498.8 𝑢𝑛𝑖𝑡𝑠 2
D.)584.6 𝑢𝑛𝑖𝑡𝑠 2
E.) 682.3 𝑢𝑛𝑖𝑡𝑠 2
Final Exam Review packet Geometry A
2014
19.) Find the area of the regular polygon. Round your answer to the nearest tenths place.
A.) 584.6 𝑚𝑖 2
B.) 102.3 𝑚𝑖 2
C.) 86.9 𝑚𝑖 2
D.) 47.0 𝑚𝑖 2
E.) 43.5 𝑚𝑖 2
20.) Find the area of the regular polygon. Round your answer to the nearest tenths place.
A.) 861.2 𝑢𝑛𝑖𝑡𝑠 2
B.) 684.6 𝑢𝑛𝑖𝑡𝑠 2
C.) 584.6 𝑢𝑛𝑖𝑡𝑠 2
D.) 474.1 𝑢𝑛𝑖𝑡𝑠 2
E.) 374.1 𝑢𝑛𝑖𝑡𝑠 2
21.) Critique the work of the student shown in the example below. Describe the mistake in
complete sentences and using accurate math computations correct the answer.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
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Final Exam Review packet Geometry A
2014
22.) Critique the work of the student shown in the example below. Describe the mistake in
complete sentences and using accurate math computations correct the answer.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
23.) Critique the work of the student shown in the example below. Describe the mistake in complete
sentences and using accurate math computations correct the answer.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
Final Exam Review packet Geometry A
2014
Chapter 12: Solids Surface Area and Volume
1.) Find the surface area of the prism.
A.) 855.07 ft2
B.) 1733.07 ft2
C.) 1342.47 ft2
D.) 2625.68 ft2
E.) 1558.07 ft2
2.) Find the surface area of the regular pyramid
A.) 1656 m2
B.) 2736 m2
C.) 4896 m2
D.) 2184 m2
E.) 1796 m2
3.) Find the surface area of the right cone
A.) 141.3 in2
B.) 266.9 in2
C.) 90 in2
D.) 167.6 in2
E.) 282.6 in2
Final Exam Review packet Geometry A
2014
4.) Find the volume of the pyramid.
A.) 1700 ft3
B.) 566.67 ft3
C.) 283.33 ft3
D.) 850 ft3
E.) 425 ft3
5.) Find the volume of the solid (in cubic meters).
A.) 780 m3
B.) 840 m3
C.) 570 m3
D.) 960 m3
E.) 440 m3
6.) Find the surface area of the right cylinder.
A.) 4647.2 cm2
B.) 2960 cm2
C.) 2323.6 cm2
D.) 1480 cm2
E.) 3265.7 cm2
7.) Find the volume of the solid.
A.) 226.08 cm3
B.) 188.4 cm3
C.) 113.04 cm3
D.) 141.3 cm3
E.) 167.3 cm3
Final Exam Review packet Geometry A
2014
8.) Which prism is similar to a prism with a length of 5 inches, width of 2 inches, and a height of 2 ½
inches?
A.) L = 4 in., w = 1 in., h = 1 ½ in.
B.) L = 10 in., w = 7 in., h = 7 ½ in.
C.) L = 10 in., w = 4 in., h = 4 ½ in.
D.) L = 2 in., w = 4/5 in., h = 1 in.
E.) L = 3 in., w = 4/5 in., h = 3 in
9.) What is the surface area of the cylinder?
A.) 94.25 ft2
B.) 106.81 ft2
C.) 175.93 ft2
D.) 347.15 ft2
E.) 530.93 ft2
10.) What is the volume of the cylinder?
A.) 20.42 ft3
B.) 40.84 ft3
C.) 81.68 ft3
D.) 265.46 ft3
E.) 530.93 ft3
11.) The surface area of the regular hexagonal pyramid is 734.12 m2. What is the slant height of the
pyramid?
A.) 8 m
B.) 9 m
C.) 10 m
D.) 12 m
E.) 14 m
Final Exam Review packet Geometry A
2014
12.) A lunch box consists of a half cylinder placed on top of a rectangular prism. What is the volume
of the lunch box?
A.) 2155 cm3
B.) 4310 cm3
C.) 6664 cm3
D.) 8819 cm3
E.) 10,974 cm3
13.) What is the relationship between the volume of a cone and the volume of a cylinder?
A.) The cone has two thirds the volume of the cylinder.
B.) The cone has one half the volume of the cylinder.
C.) The cone has one third the volume of the cylinder.
D.) The cone has one fourth the volume of the cylinder.
E.) The cone has one fifth the volume of the cylinder.
14.) What is the volume of the pyramid.
A.) 21 in3
B.) 64 in3
C.) 107 in3
D.) 192 in3
E.) 320 in3
Final Exam Review packet Geometry A
2014
15.) What is the volume of the smaller cylinder?
A.) 42.41 ft3
B.) 127.23 ft3
C.) 84.82 ft3
D.) 190.85 ft3
E.) 508.93 ft3
16.) The two cylinders above are similar. What is the volume of the larger cylinder?
A.) 71.50 ft3
B.) 95.42 ft3
C.) 169.64 ft3
D.) 226.19 ft3
E.) 301.59 ft3
17.) A cylindrical side table is packaged in the rectangular prism as shown. How much space is taken
up by the table inside the box?
Final Exam Review packet Geometry A
2014
18.) A company sells hanging lights like the one shown. The right cones are similar with a scale factor
of 3:5. The surface area of the smaller cone is approximately 6.12 square inches and the volume
of the smaller cone is approximately 31.8 cubic inches. Find the volume and surface area of the
larger cone.
19.) The leg of a couch that a company sells is formed by cutting off the top one-third of the pyramid
as shown. Using viable arguments, explain how to find the volume of the couch leg.
20.) A dining table is packaged in a box that is in the shape of a rectangular prism. The box is 5 feet
long, 3 feet wide and 1 foot deep. Find the volume and the surface area of the box.
21.) A trapezoidal desk is packaged in the box shown. Find the volume of the box.
Final Exam Review packet Geometry A
2014
Chapter 7.5 Apply the Tangent Ratio
Open End:
1. 110 inches
2. 90 ft
3. 46 ft
4. The student used cosine ratio, which is a wrong trig function in solving this problem. The correct
ratio is tangent, because the screen height is opposite 58° angle. And the person in the car is 50
ft away from the bottom of the screen. The solution should be:
tan (58°)= x/50
x = 50 tan (58°) = 80 ft
5. 598 ft.
Chapter 7.6 Apply Sine and Cosine Ratios
1.
2.
3.
4.
5.
B
A
B
E
A
Open ended:
20
x
x  37.7 feet
1. cos(58) 
a.)sin 64 
a  49.4
4.
a
55
2.
x
80
x  119 feet
tan 56 
b.) cos 64 
b  24.1
b
55
3.
Jeff :tan 56 
5. x  101.85
151
x
10, 000
x
x  20, 626.7 feet
sin 29 
Bill : tan 37 
151
y
y  200.4
Bill and Jeff are 302 feet apart
Chapter 7.7 Solving Right Triangles
1.
2.
3.
4.
5.
B
C
A
E
C
Final Exam Review packet Geometry A
2014
Chapter 8: Quadrilaterals
1. B
2. Since you can’t assume that Quadrilateral PQRS is a Rhombus, then the property that diagonals
bisect opposite angles, can’t be applied. If you were to assume that Quadrilateral PQRS is a
rectangle, then the property that all angles are 90 degrees could be applied and then x = 8
3. A
4. C
5. C
6. Since PQRS is a parallelogram then the consecutive angles are supplementary. If angle Q were
to increase, then the consecutive angles on either side of angle Q would have to decrease
keeping their sum equal to 90 degrees.
7. A
8. C
9. C
10. B
11. First I would calculate the length of the diagonal using Pythagorean’s theorem as that would
make the angles equal to 90 degrees (since Pythagorean’s theorem is only applied to right
triangles) The length of the diagonal should be approximately 3.53 meters.
12. B
13. A
14. C
15. C
16. B
17. A
18. The diagonals of a rhombus bisect each other, so the student should have made the sides of the
triangles formed inside the rhombus 5 and 12. The diagonals of a rhombus are perpendicular so
the triangles formed inside the rhombus are right, so the Pythagorean’s theorem is used. The
side lengths of the rhombus are 13, therefore the perimeter of the rhombus is 52.
19. D
20. C
21. A
22. m P & m R  1440 m S  360
QR  5cm
RS  10cm
23. B
Chapter 5: Relationships within Triangles
1.
2.
3.
4.
5.
6.
7.
D
B
C
E
C
A
C
Final Exam Review packet Geometry A
2014
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
E
D
B
D
B
A
D
D
a) MC = 22.5 b) AP = 14
a) X = 2
b) y = 8
a) YO = 6
b) Circumcenter
a) 14 cms
b) The centroid is the perfect balancing point of a triangle as it is point of concurrency of the
three medians in a triangle. The centroid divides the medians into a 2:1 ratio (or 1/3 and 2/3).
This point is also known as the center of gravity of a triangle.
Chapter 10: Circles
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
E
C
D
D
B
B
A
C
D
A
B
D
E
E
C
Open Ended
1. The other two angles measure 120o and 80 o. If a quadrilateral is inscribed in a circle,
then opposite angles in the quadrilateral are supplementary.
2.
mA  60
mB  55
mC  65
Final Exam Review packet Geometry A
2014
3.
360o  16  22.5o
4. r2 + 182 = (r + 6)2
r2 + 324 = r2 + 12r + 36
288 = 12r
r = 24
The radius of the pool is 24 feet.
5. 120o in 20 minutes ; 270o in 45 minutes
Chapter 11: Area
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
C
B
C
A
C
C
A
E
B
A
C
E
C
B
D
A
B
B
E
E
Open Ended
21. The student when using the Pythagorean theorem forgot that they needed to times their
answer by two to get the side length of the hexagon. The side length of the hexagon is
supposed to be 15 (same as the radius of the circumscribing circle!). When corrected in the
formula, the area will be 585 units squared
22. The formula for the area of a kite is the same as a rhombus. The diagonals of this kite should be
(16+5) 21 cms and (12+12) 24 cms. When the formula is applied the actual area is 252 cms
squared
23. When the probability of the shaded area, first you can find the total area of the shape which is a
rectangle. This will be your demonenator which the student calculated correctly. Then to find
the shaded region you must subtract from the rectangle the semicircle AND the little rectangle
below the semicircle which is 2(10)=20 units squared. The correct answer is (10.73/70) = 15.3%
Final Exam Review packet Geometry A
2014
Chapter 12: Surface area and Volume
Multiple Choice
1. B
2. B
3. D
4. B
5. D
6. A
7. C
8. D
9. D
10. C
11. C
12. D
13. C
14. B
15. C
16. E
Open End Questions
17. 1718.44 in3
18. 147.22 in3; 170 in2
19. Subtract the volume of the pyramid that is cut off from the main Pyramid.
20. 15 ft3 ; 46 ft2
21. 13.5 ft3
Final Exam Review packet Geometry A
2014