Geometry Semester 2 Practice Exam Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 4. A rectangular garden is to be edged with decorative brick as shown by the shaded region in the figure. The flower garden is 4 feet by 12 feet. The trapezoids are 2 feet high.
1. A tire has a radius of 15 inches. What is the approximate circumference, in inches, of the tire? A. 47 in.
8 ft
B. 94 in. C. 188 in.
2 ft
D. 707 in.
12 ft 4 ft
2. In the figure below, adjacent sides of the polygon are perpendicular. 7
7
What is the area of the decorative edge (the shaded region) in square feet?
7 15
15
A. 20 ft2 B. 26 ft2 C. 40 ft2
26
D. 48 ft2
What is the perimeter of the figure? A. 77 B. 82 C. 89 D. 96 3. The length of a rectangular patio is 32 feet. Its area is 800 square feet. What is the perimeter of the patio in feet? A. 25 ft B. 57 ft C. 114 ft D. 368 ft
2008–2009 Clark County School District
1 Revised 08/02/2011
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Geometry Semester 2 Practice Exam Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 5. Given the figure below: V
A
D F
H B
C
What is the best description of VF ? A. altitude B. base edge C. lateral edge D. slant height 6. The surface area of a cylinder is 2 × (Area of Base) + (Circumference of the Base) × height. In the cylinder below, the radius is 4 centimeters and surface area is 72π square centimeters.
What is the height of the cylinder? A. 4 cm B. 5 cm C. 6 cm D. 9 cm
2008–2009 Clark County School District
2 Revised 08/02/2011
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Geometry Semester 2 Practice Exam Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 7. A regular pyramid has height of 6 inches and the measure of the base edge is 7 inches. Volume =
1 × (Area of Base) × height 3
6 in.
7 in.
What is the volume of the pyramid? A. 49 in.3 B. 98 in.3 C. 147 in.3 D. 294 in.3
8. What is the volume of the cone below? Volume =
1 × (Area of Base) × height 3
12 in.
4 in.
A. 192π in.3 B. 96π in.3 C. 64π in.3 D. 48π in.3
2008–2009 Clark County School District
3 Revised 08/02/2011
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Geometry Semester 2 Practice Exam Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 9. A group of students wants to make a fabric toy ball to donate to the canine rescue. The diameter of the ball is 3 inches. Surface area = 4 × (Area of a Great Circle).
Approximately how many square inches of fabric will they need for each ball? A. 29 in.2 B. 57 in.2 C. 76 in.2 D. 114 in.2
10. A cereal box is 18 inches by 3 inches by 12 inches. After breakfast, the box is one-third full. Volume = (Area of Base) × height
How many cubic inches of cereal are left inside? A. 36 in.3 B. 72 in.3 C. 216 in.3 D. 648 in.3
2008–2009 Clark County School District
4 Revised 08/02/2011
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Geometry Semester 2 Practice Exam Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 11. Two similar rectangular prisms have a scale factor of 4:1. The smaller prism has a volume of 6 cubic centimeters.
13. Which accurately describes a tangent? A. A segment whose endpoints are on the circle. B. A line that intersects a circle in two points and passes through the center of the circle. C. A segment having an endpoint on the circle and an endpoint at the center of the circle.
What is the volume of the larger prism in cubic centimeters?
D. A line that intersects a circle at exactly one point.
3
A. 24 cm
B. 96 cm3
14. Use the figure below.
3
C. 384 cm
D. 1536 cm3 E
12. A pizza parlor has two different sizes of circular pizzas. The smaller one has a diameter of 12 inches and the larger one has a diameter of 20 inches.
C G B
What is the ratio of their areas? A
A. 9:25
D
B. 3:5 Which of the following represent a secant?
C. 2 3 : 2 5 D.
6 : 10
A. AG B. BE C. CA D. DA
2008–2009 Clark County School District
5 Revised 08/02/2011
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Geometry Semester 2 Practice Exam Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 15. In circle S below,
17. In
mWZ = 3 ( 2 x + 15 ) ° , and
P
m∠XLY = 148° .
32°
Q
K , m XY = ( 7 x − 9 ) ° ,
S
W X
T
K
L
R
The m∠QPT = 32° , what is the measure of ∠QRT ?
Y Z
A. 16° What is the value of x?
B. 32° C. 64°
A. 20
D. 128°
B. 54 C. 131
16. In circle J below,
D. 350
156° L
18. In the figure below, mBC = 75° and m AD = 135° ,
( 3 x − 6) ° J
A
B
K
P
Q R
What is the value of x?
C
A. 78
D
B. 54
What is m∠P ?
C. 50
A. 15°
D. 27
B. 30° C. 45° D. 60° 2008–2009 Clark County School District
6 Revised 08/02/2011
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Geometry Semester 2 Practice Exam Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 19. Two tangents are drawn from point P to circle H.
21. In
K , NK = 3 x + 4 , KW = 5 x − 8 ,
SA = 5 x − 4 , and KN ≅ KW .
N
R N
H
C
P
A K W
R
What conclusion is guaranteed by this diagram?
S
What is CN?
1 mNR = m∠NPR A. 2
A. 6
B. ΔHNR is a right triangle.
B. 13
C. HNPR is a rhombus.
C. 22
D. HNPR is a kite.
D. 26
20. All of the segments shown in the figure below are tangents to N . B T
A
10 cm
6 cm
N W
U 3 cm
4 cm D
V
C
Given the measures in the figure above, what is the perimeter of quadrilateral ABCD? A. 23 cm B. 40 cm C. 46 cm D. 52 cm 2008–2009 Clark County School District
7 Revised 08/02/2011
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Geometry Semester 2 Practice Exam Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 22. CK is the diameter of
24. How many lines of symmetry does a square have?
O,
mJC = ( 19 x ) ° , and mJK = ( 9( x + 2) − 6 ) ° .
A. 0 B. 1
C
C. 2 D. 4 O
25. Which figure contains two similar triangles that are not congruent?
J
A.
L K
What is the value of x? A.
4 5
B.
5 6
B.
C. 4 D. 6 C. 23. Determine the transformation that has mapped Δ ABC to Δ A′ B′C ′ . A
D. B'
B
C
C'
A'
A. dilation B. reflection C. rotation D. translation 2008–2009 Clark County School District
8 Revised 08/02/2011
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Geometry Semester 2 Practice Exam Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 26. The following figures are similar. W
28. The measures of the angles of a triangle have the ratio 4:6:7. What type of triangle is it?
X
A. acute
32
B. isosceles 56
Z A
C. obtuse
Y
D. right
B 24
D
42
29. The perimeter of a right triangle is 90 feet. The ratio of the legs is 5:12. What is the length of the longest leg of the triangle?
C
What is the scale factor of WXYZ to ABCD?
A. 12 ft
A. 1 to 2
B. 32 ft
B. 3 to 1
C. 36 ft
C. 3 to 2
D. 90 ft
D. 4 to 3
30. Pat measures the length of the shadow of a tree to be 54 feet long. At the same time he measures his own shadow to be 12 feet long and his height to be 5 feet. How tall is the tree in feet?
27. Two plasma screen TVs are similar rectangles. Their scale factor is 8:5. The perimeter of the smaller TV is 70 inches. The lengths of the sides of the larger TV are represented by the variable expressions shown in the diagram below.
A. 27
(3x – 4) in.
1 feet 2
B. 25 feet C. 22
(2x) in.
1 feet 2
D. 20 feet What is the value of x? A. 8 B. 12 C. 16 D. 24
2008–2009 Clark County School District
9 Revised 08/02/2011
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Geometry Semester 2 Practice Exam Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 31. Kris places a mirror on the ground. She stands so that she can see the reflection of the top of a flagpole in the mirror. G
h
2m 15 m
3m
What is the height h of the flagpole in meters? A. 10 m B. 12 m C. 18 m D. 20 m
32. Given the two triangles pictured below. N
J
H
6
9
L O
15
B
What measure for HJ would make ΔNOB ∼ ΔLJH ? A. 24
1 2
B. 13
1 2
C. 10 D. 9 2008–2009 Clark County School District
10 Revised 08/02/2011
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Geometry Semester 2 Practice Exam Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 33. In the triangle below, ∠BAC ≅ ∠CAD . B
4
C
35. What is the geometric mean of 16 and 36? A. 9
z
B. 10
D
C. 24
7
D. 26
10.5
36. Nan stands at the corner of the rectangular driveway shown below.
A
What is the value of z?
B
D
A. 6 B. 12
21 ft
C. 13.5 D. 21.5
A
34. In the triangle below, RT HS . M
x
T
C
How far must Nan walk diagonally across the driveway (A to B)?
15
A. 7 ft
S
4
28 ft
B. 14 ft
R
C. 35 ft 6
D. 49 ft H
What is the value of x? A. 9 B. 10 C. 12
1 2
D. 22
1 2
2008–2009 Clark County School District
11 Revised 08/02/2011
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Geometry Semester 2 Practice Exam Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 37. A box is shown below.
38. Use the dimensions given in the diagram below.
B 13
5 24 in.
16 x 8 in. A
6 in.
What is AB? A. 26 in. What is the value of x?
B. 38 in. C. 2 153 in.
A. 12
D. 8 10 in.
B. 20 C. 22 D. 30 39. The three sides of a triangle are 3 centimeters, 5 centimeters, and 7 centimeters. What is the best description for this triangle? A. acute triangle B. equiangular triangle C. obtuse triangle D. right triangle
2008–2009 Clark County School District
12 Revised 08/02/2011
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Geometry Semester 2 Practice Exam Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 40. A jet is flying 7 miles above the ground. The pilot spots an airport as shown below.
42. In rectangle ABCD, BD = 12 and m∠ABD = 30° . What is the length of the longer side of the rectangle? A. 6 B. 12 C. 6 2
7 mi
d
D. 6 3 45°
43. Use the table and the dimensions given in the diagram below.
What is the distance d from the plane to the airport?
50°
A. 7 2 mi
10
B. 7 3 mi C. 7 mi
r
D. 14 mi
θ 20° 30° 40° 50°
41. Use the dimensions given in the diagram below.
sin θ .3420 .5000 .6428 .7660
cos θ .9397 .8660 .7660 .6428
tan θ .3640 .5774 .8391 1.1918
What is the value of r?
4 45°
A. 11.918
30°
B. 8.391
y
C. 7.660
What is the value of y?
D. 6.428
A. 4 3 B. 2 3 C. 4 6 D. 2 6
2008–2009 Clark County School District
13 Revised 08/02/2011
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Geometry Semester 2 Practice Exam Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 44. Use the dimensions given in the right triangle below.
46. Use the dimensions given in the diagram below.
B 15
A
9 12
C
What is the cosine of ∠A ? A.
h
9 12
B.
9 15
C.
12 9
53° 150 ft
Which equation would be used to find the distance h from the hot air balloon to the ground? A. h = 150 tan 53°
12 D. 15
B. h = 150sin 53°
45. Use the table and the dimensions given in the diagram below.
C. h =
150 tan 53°
D. h =
150 sin 53°
Angle of descent 10 mi
3.4 mi
θ 20° 30° 40° 50°
sin θ .3420 .5000 .6428 .7660
cos θ .9397 .8660 .7660 .6428
tan θ .3640 .5774 .8391 1.1918
What is the approximate angle of descent? A. 50° B. 40° C. 30° D. 20°
2008–2009 Clark County School District
14 Revised 08/02/2011
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Geometry Semester 2 Practice Exam Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 47. Use the table and the dimensions given in the diagram below.
48. In circle D below, AB is tangent to D at A, and CB is tangent to D at C. A 2x – 6
10
B
d
D
128 ft 3( x − 7)
40°
θ 20° 30° 40° 50°
C sin θ .3420 .5000 .6428 .7660
cos θ .9397 .8660 .7660 .6428
tan θ .3640 .5774 .8391 1.1918
What is the length of BD ? A. 14 B. 15 C. 24
What is the approximate length d of the kite string?
D. 26
A. 256 ft
49. In the figure below, AB is tangent to D at A and BC is tangent to D at C.
B. 200 ft C. 168 ft D. 100 ft
A
2 ( x + 5) − 1
B
6 D
5x C
What is the value of x? A. 2 B. 3 C. 4 D. 5
2008–2009 Clark County School District
15 Revised 08/02/2011
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Geometry Semester 2 Practice Exam Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 50. In the figure below, RP is tangent to the circle at R and SP is a secant. R x P
V
6 cm
8 cm S
What is the value of x? A. 48 cm B. 84 cm C. 4 3 cm D. 2 21 cm
2008–2009 Clark County School District
16 Revised 08/02/2011
Geometry 2011–2012 Semester 2 Free Response Practice Exam OK
Note: Diagrams on this exam are not necessarily drawn to scale.
Calculators allowed
1. Given triangle ABD with altitude BC , what are the following measures? B
BC = ________ CD = _______
45° 8 2
AB = ________ m ∠A = ________ A
15
D
C
2. Given that pentagon ABCDE ~ pentagon VWXYZ, find the following values: Scale factor of ABCDE to VWXYZ. ________
C
ED = ________
30°
VZ = ________
V 66°
B
5
A
m∠Z = ________
W
6 D
CB = ________ VW = ________
Z
4
104°
2
X
3
Y
4 84° E
3. Given circle A with diameters of CD and EB , and FE is tangent to circle A at point E. What are the following measures? C m∠1 = ________
2 E
m∠2 = ________
3
m∠3 = ________ 1
m∠4 = ________
130°
A
m∠5 = ________
7
F
G
m∠6 = ________ m∠7 = ________
5 4 70° D
2011–2012 Clark County School District
1 Revised 10/11/2011
6
B
GEOMETRY SEMESTER 2 EXAM ITEM SPECIFICATION SHEET & KEY Free Response #
Syllabus Objectives
Course Concepts / Objectives
1
Right Triangles and Trigonometry
2
Similarity
3
Perimeter and Area Circles
7.1–7.7 6.1–6.6 7.2 8.1–8.2 10.1–10.6
NV State Standards 4.12.2 4.12.7 3.12.5 4.12.2 3.12.5 4.12.1
# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Objective Solve problems using perimeters or areas of geometric figures. Solve problems using perimeters or areas of geometric figures. Solve real world problems of perimeter and area. Solve real world problems of perimeter and area. Compare attributes of various geometric solids. Solve surface area and volume problems of various geometric solids. Solve surface area and volume problems of various geometric solids. Solve surface area and volume problems of various geometric solids. Solve real world problems of surface area and volume. Solve real world problems of surface area and volume. Solve area and volume problems of similar two and three dimensional figures. Solve area and volume problems of similar two and three dimensional figures. Differentiate among the terms relating to a circle. Differentiate among the terms relating to a circle. Solve problems involving angles, arcs, or sectors of circles. Solve problems involving angles, arcs, or sectors of circles. Solve problems involving arcs, chords, and radii of a circle. Solve problems involving arcs, chords, and radii of a circle. Explore relationships among circles and external lines or rays. Explore relationships among circles and external lines or rays. Solve problems involving properties of circles using algebraic techniques.
2011–2012 Clark County School District
Syllabus Objective
NV State Standard
Key
8.2
3.12.5
B
8.2
3.12.5
D
8.3 8.3 9.1
3.12.5 3.12.5 3.12.5
C C A
9.2
3.12.5
B
9.2
3.12.5
B
9.2
3.12.5
C
9.3
3.12.5
A
9.3
3.12.5
C
9.4
3.12.5
C
9.4
3.12.5
A
10.1 10.1
4.12.1 4.12.1
D A
10.2
4.12.1
B
10.2
4.12.1
B
10.3
4.12.1
A
10.3
4.12.1
B
10.4
4.12.1
D
10.4
4.12.1
C
10.5
4.12.1
B
Page 1 of 3
Revised: 09/28/2011
GEOMETRY SEMESTER 2 EXAM ITEM SPECIFICATION SHEET & KEY
# 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47
Objective Solve problems involving properties of circles using algebraic techniques. Distinguish among the basic mapping functions: dilations, reflections, translations, and rotations. Differentiate between examples of each type of symmetry. Differentiate between similar and congruent. Determine scale ratios and write appropriate proportions. Solve proportion problems using algebraic techniques. Solve proportion problems using algebraic techniques. Solve proportion problems using algebraic techniques. Formulate and solve real world problems using similar triangles. Formulate and solve real world problems using similar triangles. Prove that two triangles are similar. The student will explore properties of proportionality within a triangle. The student will explore properties of proportionality within a triangle. Explore geometric mean relationships within a right triangle. Solve problems using the Pythagorean Theorem. Solve problems using the Pythagorean Theorem. Solve problems using the Pythagorean Theorem. Solve problems using the converse of the Pythagorean Theorem and related theorems for obtuse or acute triangles. Solve problems using the converse of the Pythagorean Theorem and related theorems for obtuse or acute triangles. Solve problems utilizing the ratios of the sides of special right triangles. Solve problems utilizing the ratios of the sides of special right triangles. Define and apply basic trigonometric ratios of sine, cosine, and tangent. Define and apply basic trigonometric ratios of sine, cosine, and tangent. Solve problems using the trigonometric ratios. Solve problems using the trigonometric ratios. Solve problems using the trigonometric ratios.
2011–2012 Clark County School District
Syllabus Objective
NV State Standard
Key
10.5
4.12.1
D
11.1
4.8.1
C
11.4
4.8.3
D
6.1
4.12.1
A
6.2
4.12.2
D
6.4
3.12.5
B
6.4
3.12.5
A
6.4
3.12.5
C
6.5
3.12.5
C
6.5
3.12.5
A
6.6
4.12.2 4.12.2 4.12.9 4.12.2 4.12.9
C
6.7 6.7
A B
7.2
4.12.2
C
7.3 7.3 7.3
4.12.7 4.12.7 4.12.7
C A B
7.4
4.12.7
A
7.4
4.12.7
A
7.5
4.12.2
D
7.5
4.12.2
D
7.6
4.12.2
A
7.6
4.12.2
D
7.7 7.7 7.7
4.12.2 4.12.2 4.12.2
D A B
Page 2 of 3
Revised: 09/28/2011
GEOMETRY SEMESTER 2 EXAM ITEM SPECIFICATION SHEET & KEY
# 48 49 50
Objective Solve problems involving secant segments and tangent segments for a circle. Solve problems involving secant segments and tangent segments for a circle. Solve problems involving secant segments and tangent segments for a circle.
Syllabus Objective
NV State Standard
Key
10.6
4.12.1
D
10.6
4.12.1
B
10.6
4.12.1
D
2011–2012 Clark County School District
Page 3 of 3
Revised: 09/28/2011
