Student’s Name Student ID No. Address
Geometry Part 2 Examination
Comprehensive Examination for Lessons 4, 5, and 6
Please read these instructions before you begin to answer the questions that follow.
Write your answers and your work on this examination. When you are satisfied that your answers are correct, write them on the Answer Sheet found right after the exam. Then send the Answer Sheet only (not the exam itself) to The Keystone School for grading. Attach separate paper for your work if necessary. Good Luck!
1. Solve:
a. 2 b. 3 c. 8 d. 12.5
2. Solve:
a. 5 b. 2.5 c. 10 d. 4
A man walked 7 miles in 1.5 hours. How many miles will he travel in 6 hours going at the same rate?
a. 9 b. 28 c. 42 d. 10.5
Polygon ABCDE is similar to polygon VWXYZ, and AB = 10, VW = 15. If BC = 5, then
WX = ?
a. 7.5 b. 1.2 c. 3.33 d. 30
A building casts a 200 ft. long shadow. At the same time, your shadow is 5 feet long. You are 6 feet tall. How tall is the building?
a. 6.7 ft. b. 100ft. c. 166.6ft. d. 240 ft.
For questions 6-8, use the following diagram.
What reason justifies why triangle ABC is similar to triangle ADE?]
SSS b. AA c. SAS d. the triangles are not similar
Find x.
a. 4 b. 5 c. 6 d. 8
Find y.
a. 10 b. 4 c. 5 d. 2.5
Find the geometric mean between 5 and 8.
a. √13 b. 13 c. 6.5 d. 2√10
Find the geometric mean between 7 and 11.
a. √77 b. 4 c. 9 d. √18
For questions 11 and 12, refer to the following triangle.
If e = 8 and f = 4, find d.
a. 16 c. 32
b. 12 d. 4
If b = 5 and d = 4, find c.
a. 1 c. 6.25
b. 20 d. 9
Determine if the given measures are sides of a right triangle: 9, 10, 15
yes b. no
The length of a rectangle is 3 cm and the width is 2 cm. Find the length of the diagonal.
5cm b. 6 cm c. √5 cm d. √13 cm
For questions 15 and 16, use the following triangle.
If a = 10 and c = 26, find b.
a. 18 b. 4 c. 6 d. 24
If a = 5 and c = 8, find b.
a. √39 b. √89 c. 2√10 d. 9
The hypotenuse of a 30-60-90 degree right triangle measures 12. What is the measure of the shortest side?
a. 12√3 b. 6 c. 6√3 d. 24
The perimeter of a square is 12 cm. Find the length of a diagonal.
3 cm b. 3√3 cm c. 3√2 cm d. 4√3 cm
If a = 4, find b.
4 c. 2
b. 4√2 d. 4√3
If b = 6, find c.
a. 6 b. 12 c. 6√3 d. 6√2
For questions 21 and 22, use the following triangle.
Find sin A.
4
a.
3
4 3
3
3
.
.c. d
5 5 4
Find cos A.
4
a.
3
4 3
3
3
.
.b. c. d
5 5 4
cos A = .7986, find angle A.
79 degrees c. 53 degrees
38 degrees d. 37 degrees
tan R = 4.0108, find angle R.
76 degrees c. 4 degrees
14 degrees d. 90 degrees
If the radius of a circle is 3.1, find the circumference.
a. 6.2 𝜋 b. 3.1 𝜋 c. 6.2 d. 3.1
If the diameter of a circle is 10, find the circumference.
a. 20 𝜋 b. 10 𝜋 c. 20 d. 10
Write an equation for a circle with center at P(2, -5) and a diameter of 8 units. a. (x – 2)2 + (y – 5)2 = 64 c. (x – 2)2 + (y + 5)2 = 16
b. (x + 2)2 + (y + 5)2 = 8 d. (x + 2)2 + (y – 5)2 = 16
For questions 28-30, refer to the following diagram.
Name the arc with measure of 140 degrees.
arc DEB b. arc ABC c. arc CDE d. arc ABD
If AD = 10, find the length of arcEDC.
a. 45 𝜋 b. 45 c. d. 5 𝜋
Find measure of arc BCD.
130 degrees b. 230 degrees c. 180 degrees d. 90 degrees
For questions 31 and 32, use the following diagram.
Find the measure of arc BC.
a. 35 c. 17.5
b. 70 d. 75
Find m<ADB.
a. 75 c. 40
b. 35 d. 4
For problems 33 and 34, use the following diagram. AB is a tangent, AD and AE are secants.
Find AC.
a. 13 c. 26
b. 22 d. 20
Find m<DAE.
20 degrees b. 25 degrees c. 40 degrees d. 60 degrees
Find the circumference of a circle with a radius of 6 in.
6 in. c. 6 𝜋 in.
b. 12 in. d. 12 𝜋 in.
Find the area of a circle with a diameter of 20 yd.
10 square yd c. 10 𝜋 square yd
100 square yd d. 100 𝜋 square yd
Find the area of a sector defined by a central angle of 120 degrees and a radius of 6 cm.
3 𝜋 square cm c. 12 𝜋 square cm
6 𝜋 square cm d. 36 𝜋 square cm
The base of a right rectangular prism is 10 ft by 6 ft. The height is 4 ft. Find the surface area.
124 square feet c. 152 square feet
240 square feet d. 248 square feet
The slant height of a regular pentagonal pyramid is 8 cm and the length of each side of the base is 4 cm. Find the lateral area.
32 square cm c. 80 square cm
60 square cm d. 160 square cm
For problems 40 and 41, use the following diagram of the right cylinder.
If r = 4 yd and h = 5 yd, find the lateral area.
20 𝜋 square yd c. 9 𝜋 square yd
16 𝜋 square yd d. 40 𝜋 square yd
If r = 4 yd and h = 5 yd, find the surface area.
41 𝜋 square yd c. 72 𝜋 square yd
48 𝜋 square yd d. 80 𝜋 square yd
For problems 42-44, use the following diagram of the right cone.
If r = 3 in. and h = 4 in., find the slant height.
25 in. c. 7 in.
12 in. d. 5 in.
If r = 3 in. and h = 4 in., find the lateral area.
15 𝜋 square in. c. 20 𝜋 square in.
12 𝜋 square in. d. 4 𝜋 square in.
If r = 3 in. and h = 4 in., find the total surface area.
32 𝜋 square in. c. 21 𝜋 square in.
20 𝜋 square in. d. 24 𝜋 square in.
The volume of a cube is 27 cubic inches. Find the surface area.
9 square inches c. 54 square inches
27 square inches d. 108 square inches
Find the surface area of a sphere with a radius of 4 inches.
211/3 square inches c. 16 𝜋 square inches
64 square inches d. 256 𝜋 square inches
For problems 47 and 48, use the following diagram of the right cylinder.
If r = 4 m and h = 5 m, find the volume.
24 cubic meters c. 16 𝜋 cubic meters
40 cubic meters d. 80 𝜋 cubic meters
If volume = 400 𝜋 cubic yards and h = 4 yd, find the radius.
8 yards c. 12 yards
10 yards d. 20 yards
For problems 49 and 50, use the following diagram of the right circular cone.
If h = 4 cm and r = 3 cm, find the volume.
12 cubic cm c. 18 𝜋 cubic cm
6 cubic cm d. 24 𝜋 cubic cm
If volume = 100 𝜋 cubic cm and h = 12, find the radius.
5 cm c. 10 cm
8 cm d. 12 cm
Find the volume of a sphere with a radius of 3 in.
9 𝜋 square in. c. 36 𝜋 square in.
27 𝜋 square in. d. 81 𝜋 square in.
If two solids are similar and have a linear ratio of 2:5, what is the ratio of the areas? a. 4:25 c. 4:5
b. 2:5 d. 2:25
If the ratio of areas of two similar solids is 25:36, what is the linear ratio? a. 50:72 c. 5:6
b. 6:5 d. 1:11
Find the area of a circle with a radius of 2.9 yd.
18.2 square yd. c. 105.6 square yd.
b. 26.4 square yd. d. 422.5 square yd.
If the area of a circle is 36 𝝅 square cm, find the diameter.
a.12 cm c. 144 cm
b. 36 cm d. 24 cm
Find the area of a circle with a circumference of 27 ft. Round to the nearest whole number.
a. 48 c. 58
b. 50 d. 68
Find the circumference of a circle with radius of 4.2 in.
a. 13.2 in. c. 55.4 in.
b. 26.4 in. d. 6.6 in.
If the area of a circle is 40 𝝅 square cm, find the radius.
a.10 cm c. 20 cm
b. 2√5 cm d. 2√10 cm
Find the coordinate of the image of the point (4, 2) dilated with center at the origin, scale factor ½. a. (8,4) b. (-4,2) c. (2,1) d. (2,4)
Which type of dilation is determined by a scale factor 2/3?
a. enlargement c. congruence transformation
c. reduction d. none of these
Find the coordinate of the image of the point (-3, -1) dilated with center at the origin, scale factor 2.
a. (1.5, .5) c. (-6, -2)
b. (6, 2) d. (-1.5, -.5)
The measure of an inscribed angle equals
half the measure of the intercepted arc.
twice the measure of the intercepted arc.
twice the measure of the corresponding central angle.
the measure of the corresponding central angle.
To find the lateral area of a regular pyramid, you need to know the slant height and the
altitude. c. area of the base.
surface area. d. perimeter of the base.
Which type of dilation is determined by a scale factor of 10?
enlargement c. congruence transformation
reduction d. none of these
If triangle ABC is similar to triangle LMN, AB =18, BC = 12, LN =9, and LM =6.
What is the scale factor of triangle ABC to triangle LMN?
a. 9:2 b. 3:2 c. 3:1 d. 2:1
Given the choice between doing an oral and a written report, 18 of the 28 students chose to do an oral report. Find the ratio of written to oral reports.
a. 5:9 b. 9:5 c. 9:14 d. 14:9
A model of a lighthouse has diameter 8 inches and height 18 inches. If the actual diameter of the lighthouse is 20 feet, find its actual height.
a. 30 ft. b. 35 ft. c. 45 ft. d. 50 ft.
Find the polygon that is similar to ABCD.
b. c. d.
Use the above diagram to complete questions 69-71.
Name a diameter.
a.
b.
c.
d.
Name a chord.
a.
b.
c.
d.
Name a secant.
a.
b.
c.
d.
The diameter of a circular swimming pool is 15 feet. Find the circumference to the nearest hundredth.
a.
47.12 ft
b.
63.81 ft
c.
75.96 ft
d.
94.24 ft
In A, m BAD = 110. Find .
a.
180
b.
55
c.
70
d.
110
Points X and Y lie on P so that PX = 5 meters and m XPY = 90. Find the length of to the nearest
a.
3.93 m
b.
7.85 m
c.
15.71 m
d.
19.63 m
Chords and are equidistant from the center of O. If XY = 2x + 30 and WV = 5x – 12, find x.
a.
58
b.
28
c.
14
d.
6
Find the radius of O if DE = 12 inches and bisects .
a.
in.
b.
6 in.
c.
8 in.
d.
in.
Find x.
a.
122
b.
61
c.
58
d.
29
EFGH is a quadrilateral inscribed in P with E = 72 and F = 49. Find H.
a.
131
b.
108
c.
90
d.
57
If is tangent to C at A, find BC.
a.
6 in.
b.
in.
c.
in.
d.
24 in.
, , , and are tangent to X. Find RS.
a.
9 in.
b.
12 in.
c.
13 in.
d.
cannot tell
Circle A has its center at A(3, 2), and is tangent to A at B(6, 4). Find the slope of .
a.
b.
c.
d.
Find x.
a.
78
b.
90
c.
102
d.
204
Find .
a.
66
b.
57
c.
45
d.
21
Find z.
a.
2
b.
4.5
c.
7
d.
8
Find ZC.
a.
4
b.
16
c.
22
d.
32
Find the center of the circle whose equation is (x + 11)2 + ( y – 7)2 = 121.
a.
(–11, 7)
b.
(11, –7)
c.
(121, 49)
d.
11
Find the equation of a circle whose center is at (2, 3) and radius is 6.
a.
(x + 2)2 + ( y + 3)2 = 6
b.
(x – 2)2 + ( y – 3)2 = 6
c.
(x + 2)2 + ( y + 3)2 = 36
d.
(x – 2)2 + ( y – 3)2 = 36
Find the equation of P.
a.
x2 + ( y – 3)2 = 4
b.
x2 + ( y – 3)2 = 2
c.
(x – 3)2 + y2 = 2
d.
(x – 3)2 + y2 = 4
Refer to the figure below to answer the following questions.
Identify this solid figure.
a.
square pyramid
b.
square prism
c.
triangular pyramid
d.
triangular prism
Name the base.
a.
ABE
b.
ABCD
c.
CDE
d.
E
The shape of a vertical cross section of a cone is a .
a.
circle
b.
triangle
c.
square
d.
trapezoid
Find the surface area of the cube.
a.
9 in2
b.
27 in2
c.
36 in2
d.
54 in2
Refer to the figure below to answer the following questions.
Find the lateral area. Round to the nearest tenth.
a.
75.4 ft2
b.
62.8 ft2
c.
50.3 ft2
d.
25.1 ft2
Find the surface area. Round to the nearest tenth.
a.
75.4 ft2
b.
62.8 ft2
c.
50.3 ft2
d.
25.1 ft2
Refer to the figure below to answer the following questions.
Find the lateral area.
a.
108 cm2
b.
144 cm2
c.
162 cm2
d.
324 cm2
Find the surface area.
a.
108 cm2
b.
144 cm2
c.
162 cm2
d.
324 cm2
Find the surface area to the nearest tenth.
a.
546.6 units2
b.
989.6 units2
c.
1017.9 units2
d.
1046.2 units2
The radius of a cone is 17 inches long and the slant height is 20 inches. Find the surface area to the nearest tenth.
a.
18,158.4 in2
b.
1976.1 in2
c.
1068.1 in2
d.
340 in2
The area of the base of a prism is 96 square centimeters and the height is 9 centimeters. Find the volume of the prism.
a.
288 cm3
b.
864 cm3
c.
932 cm3
d.
7776 cm3
At a certain time of day, a 5.5-foot tall man has a 6-foot shadow. If a tree is 19.25 feet tall, what is the length of the shadow of the tree?
a. 17.14 ft. c. 15 ft.
b. 21 ft. d. 21.1 ft.
Congratulations! You have reached the end of this course.
Congratulations! You have reached the end of this course.
