obsolete geometry semester 2 exam compilation...

Obsolete Geometry Semester 2 Exam Compilation2008–2011

The 2008 to 2012 Geometry and Geometry Honors practice semester exams are no longer available in the CPD Mathematics folder in Interact. However, teachers can use the Geometry Compilation documents for extra practice problems in their daily lesson. These documents are made up of previous years’ practice semester exams and released semester exams. Each objective is made up of four problems that have been compiled from practice exams created in 2008 and the released exams from June of 2009, 2010, and 2011.

These problems are not intended to be used as study guides for this year’s Geometry semester exams as they sometimes do not align to the district’s newly adopted Common Core State Standards for Geometry. Instead, teachers are encouraged to use this resource to provide students with more practice of a specific skill or as a long term memory review tool.

Each set of four problems begins with the district syllabus objective (now obsolete), then is followed by a problem from the 2008 practice test, one problem from the released 2009 semester exam, one problem from the released 2010 semester exam and one problem for the released 2011 semester exam.

In order to identify which year each problem comes from, the number after the dash will specify the origin of that problem. For example, #17 will begin with the syllabus objective in bold letters then will be followed by four problems: (17-8), (17-9), (17-10) and (17-11). The number after the dash indicates the year that problem was created and used. (17-8) is #17 from the 2008 practice test, (17-9) is #17 from the released 2009 semester exam etc.

New Geometry practice problems that align to the CCSS Geometry standards will be posted soon in interact.


(1) 8.2 Solve problems using perimeters or areas of geometric figures.

(1-8) A tire has a radius of 15 inches. What is the approximate circumference, in inches, of the tire?

(A) 47 in

(B) 94 in

(C) 188 in

(D) 707 in

(1-9) A circular steering wheel has a radius of 7 inches. What is the approximate circumference of the steering wheel in inches?

(A) 22 inches

(B) 44 inches

(C) 88 inches

(D) 154 inches

(1-10) A circular pond has a radius of 14 feet. Find the approximate circumference of the pond.

(A) 44 ft

(B) 88 ft

(C) 196 ft

(D) 615 ft

(1-11) A circle has a circumference of 36π centimeters. What is the radius of the circle?

(A) 6 cm

(B) 12 cm

(C) 18 cm

(D) 36 cm

26

15

7

77

15

7

11

13

27

6

8

15

12

28 cm

16 cm



(2-8) In the figure below, adjacent sides of the polygon are perpendicular.

What is the perimeter of the figure?

(A) 77

(B) 82

(C) 89

(D) 96

(2-9) In the figure, the adjacent sides of the polygon are perpendicular.


(A) 58

(B) 77

(C) 80

(D) 91

(2-10) In the figure, the adjacent sides of the polygon are perpendicular.


(A) 27 units

(B) 41 units

(C) 50 units

(D) 54 units

(2-11) In the figure below, the adjacent sides of the polygon are perpendicular.

What is the perimeter of the polygon?

(A) 93 cm

(B) 109 cm

(C) 116 cm

(D) 121 cm

5 m13 m

4 ft12 ft

2 ft

8 ft


(3) 8.3 Solve real world problems of perimeter and area.

(3-8) 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

(3-9) The length of a rectangular garden is 60 feet. Its area is 2400 square feet. What is the perimeter of the garden in feet?

(A) 100 feet

(B) 200 feet

(C) 2440 feet

(D) 2460 feet

(3-10) The width of a rectangular field is 400 meters. The area is 320,000 square meters. What is the perimeter of the field?

(A) 160 m

(B) 800 m

(C) 1200 m

(D) 2400 m

(3-11) Determine the area of the right triangular garden.

(A) 18 m2

(B) 30 m2

(C) 60 m2

(D) 65 m2


(4-8) 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.

What is the area of the decorative edge (the shaded region) in square feet?

(A) 20 ft2

(B) 26 ft2

(C) 40 ft2

(D) 48 ft2

8 ft

12 ft

2 ft


(4-9) A square flower garden is to be edged with decorative brick as shown by the shaded regions in the figure.

The flower garden is 12 feet by 12 feet. The shaded regions are 2 feet high and the outer edges parallel to the square are 8 feet long.

What is the area of the decorative edge (the shaded region) in square feet?

(A) 22 ft2

(B) 80 ft2

(C) 144 ft2

(D) 192 ft2

5 m

50 mFlowerGarden

Grass

40 m

5 m

5 m

5 m

12 in

16 in

3 in3 in

2 in

2 in


(4-10) A rectangular flower garden is surrounded by a grass border as shown. The grass border is 5 meters wide on all sides of the flower garden and the outer dimensions of the border are 50 meters by 40 meters.

Determine the area of the grass border.

(A) 90

(B) 425

(C) 800

(D) 1200

(4-11) A framed picture is shown below.

What is the area of the picture (without the frame)?

(A) 60 in2

(B) 80 in2

(C) 96 in2

(D) 192 in2

FH

V

D

CB

A

FH

V

D

CB

A

FH

V

D

CB

A

FH

V

D

CB

A


(5) 9.1 Compare attributes of various geometric solids.

(5-8) Given the figure below:

What is the best description of ?

(A) altitude

(B) base edge

(C) lateral edge

(D) slant height

(5-9) Given the figure below,

What is the best description of in relation to the pyramid?

(A) base edge

(B) height

(C) lateral edge

(D) slant height

(5-10) What is the best description of in relation to the pyramid?

(A) base edge

(B) height

(C) lateral edge

(D) slant height

(5-11) What is the best description of in relation to the pyramid?

(A) base edge

(B) slant height

(C) lateral edge

(D) altitude

6 cm

2 cm

4 cm

3 cm


(6) 9.2 Solve surface area and volume problems of various geometric solids.

(6-8) 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 72 square centimeters.

What is the height of the cylinder?

(A) 4 cm

(B) 5 cm

(C) 6 cm

(D) 9 cm

(6-9) The surface area of a cylinder is:

2 (Area of Base) + (Circumference of the Base) height

In the cylinder below, the radius is 5 centimeters and the height is 3 centimeters.

What is the surface area of the cylinder in terms of π?

(A) 30π cm2

(B) 50π cm2

(C) 75π cm2

(D) 80π cm2

(6-10) The surface area of a cylinder is given

by the formula .

What is the surface area of the cylinder above?

(A) 24π cm2

(B) 48π cm2

(C) 72π cm2

(D) 96π cm2

(6-11) The volume of a cylinder is given by the formula .

What is the volume of the cylinder?

(A) 36π cm3

(B) 48π cm3

(C) 72π cm3

(D) 192π cm3

6 in

7 in

4 in

6 in

6 in

8 in

4 in

12 cm

5 cm

13 cm



(7-8) A regular pyramid has height of 6 inches and the measure of the base edge is 7 inches.

Volume = (Area of Base) height

What is the volume of the pyramid?

(A) 49 in3

(B) 98 in3

(C) 147 in3

(D) 294 in3

(7-9) A square pyramid has height of 4 inches and the measure of the base

edge is 6 inches. Volume = (Area of Base) height


(A) 16 in3

(B) 48 in3

(C) 96 in3

(D) 144 in3

(7-10) The volume of the rectangular pyramid below is given by the formula

.


(A) 64 in3

(B) 72 in3

(C) 128 in3

(D) 192 in3

(7-11) The surface area of a square pyramid is

given by the formula .

What is the surface area of the pyramid?

(A) 285 cm2

(B) 300 cm2

(C) 340 cm2

(D) 360 cm2

4 in

12 in

3 in.

9 in.

4 ft

6 ft

3 cm

4 cm

5 cm



(8-8) What is the volume of the cone below?


(A) 192π in3

(B) 96π in3

(C) 64π in3

(D) 48π in3

(8-9) A cone has a height of 9 inches and a radius of 3 inches.


What is the volume of the cone in terms of ?

(A) 108π in3

(B) 81π in3

(C) 27π in3

(D) 18π in3

(8-10) The volume of a cone is given by the

formula .

What is the volume of the cone?

(A) 8π ft3

(B) 32π ft3

(C) 48π ft3

(D) 96π ft3

(8-11) The surface area of a cone is given by the formula .

What is the surface area of the cone?

(A) 24π cm2

(B) 21π cm2

(C) 18π cm2

(D) 9π cm2


(9) 9.3 Solve real world problems of surface area and volume.

(9-8) 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 in2

(B) 57 in2

(C) 76 in2

(D) 114 in2

(9-9) The diameter of a softball is approximately four inches.

Surface area of a Sphere = 4 (Area of a Great Circle)

Approximately how many square inches of leather are needed to cover the ball?

(A) 15 in2

(B) 50 in2

(C) 85 in2

(D) 250 in2

(9-10) A bubble forms a sphere with a radius of 3 cm.

What is the volume of air inside the bubble?

(A) 12π cm3

(B) 24π cm3

(C) 36π cm3

(D) 108π cm3

(9-11) A small spherical ball has a diameter of 6 centimeters. What is the surface area of the ball?

(A) 144π cm2

(B) 48π cm2

(C) 36π cm2

(D) 24π cm2

10 cm

4 cm



(10-8) A cereal box is 18 inches by 3 inches by 12 inches. After breakfast, the box is one-third full.


How many cubic inches of cereal are left inside?

(A) 36 in3

(B) 72 in3

(C) 216 in3

(D) 648 in3

(10-9) A cereal box is 10 inches by 2 inches by 15 inches. After breakfast, the box is half full.

How many cubic inches of cereal are left inside?

(A) 75 in3

(B) 150 in3

(C) 300 in3

(D) 600 in3

(10-10) A box of sugar in the shape of a rectangular prism measures 6 inches by 2 inches by 10 inches. After some

sugar is used, the box is full.

How many cubic inches of sugar were used?

(A) 12 in3

(B) 18 in3

(C) 40 in3

(D) 80 in3

(10-11) Water is poured into a cylindrical container until it is half full.

What is the volume of the water?

(A) 14π cm3

(B) 20π cm3

(C) 80π cm3

(D) 160π cm3


(11) 9.4 Solve area and volume problems of similar two and three dimensional figures.

(11-8) Two similar rectangular prisms have a scale factor of 4:1. The smaller prism has a volume of 6 cubic centimeters.

What is the volume of the larger prism in cubic centimeters?

(A) 24 cm3

(B) 96 cm3

(C) 384 cm3

(D) 1536 cm3

(11-9) Two similar rectangular prisms have a scale factor of 3:1. The larger prism has a volume of 135 cubic centimeters.

What is the volume of the smaller prism in cubic centimeters?

(A) 5 cm3

(B) 15 cm3

(C) 25 cm3

(D) 45 cm3

(11-10) Two similar nonagons have a scale factor of 5:3. The smaller nonagon has an area of 90 .

What is the area of the larger nonagon?

(A) 19 m2

(B) 30 m2

(C) 150 m2

(D) 250 m2

(11-11) Two similar pentagons have a scale factor of 3:4. The larger pentagon has an area of 32 square feet.

What is the area of the smaller pentagon?

(A) 8 ft2

(B) 12 ft2

(C) 18 ft2

(D) 24 ft2

16 in.12 in.

16 in.10 in.


(12) 9.4 Solve area and volume problems of similar two and three dimensional figures.

(12-8) 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. What is the ratio of their areas?

(A) 9:25

(B) 3:5

(C)

(D)

(12-9) A pizza parlor has two different sizes of pizza. The smaller one has a diameter of 10 inches and the larger one has a diameter of 18 inches. What is the ratio of their areas?

(A)

(B)

(C)

(D)

(12-10) A pizza parlor has two different sizes of pizza. The smaller one has a diameter of 12 inches and the larger one has a diameter of 16 inches.

What is the ratio of the area of the smaller pizza to the area of the larger pizza?

(A)

(B)

(C) 3:4

(D) 9:16

(12-11) A pizza parlor has two different sizes of pizza. The smaller one has a diameter of 10 inches and the larger one has a diameter of 16 inches.

What is the ratio of the area of the smaller pizza to the area of the larger pizza?

(A) 5:8

(B) 10:16

(C) 25:64

(D) 125:512


(13) 10.1 Differentiate among the terms relating to a circle.

(13-8) 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.

(D) A line that intersects a circle at exactly one point.

(13-9) Which accurately describes a secant?

(A) A line that intersects a circle at two points.

(B) A segment whose endpoints are on the circle.

(C) A segment having an endpoint on the circle and an endpoint at the center of the circle.


(13-10) Which accurately describes a chord?

(A) A segment whose endpoints are points on the circle.

(B) A segment having an endpoint on the circle and an endpoint at the center of the circle.

(C) A line that intersects a circle at two points.


(13-11) Which accurately describes a radius?

(A) A line that intersects a circle at two points.

(B) A line that intersects a circle at exactly one point.

(C) A segment whose endpoints are points on the circle.

(D) A segment having an endpoint on the circle and an endpoint at the center of the circle.

G

E

D

C

B

A

G

E

D

C

B

A

G

E

D

C

B

A

G

E

D

CB

A


(14) 10.1 Differentiate among the terms relating to a circle.

(14-8) Use the figure below.

Which of the following represent a secant?

(A)

(B)

(C)

(D)

(14-9) Use the figure below.

Which represents a chord?

(A)

(B)

(C)

(D)

(14-10) Use the figure.

Which represents a tangent?

(A)

(B)

(C)

(D)

(14-11) Use circle C.

Which is a diameter?

(A)

(B)

(C)

(D)

32°

P

R

T

Q

S

86°

P

R

T

Q

O

P

R

T

Q

O

38º

P

R

T

Q

O

82°


(15) 10.2 Solve problems involving angles, arcs, or sectors of circles.

(15-8) In circle S below,

The , what is the measure of ?

(A) 16°

(B) 32°

(C) 64°

(D) 128°

(15-9) Use circle O below.

Since , what is the measure of ?

(A) 43°

(B) 86°

(C) 90°

(D) 172°

(15-10) Use circle O.

Since , what is ?

(A) 19°

(B) 38°

(C) 42°

(D) 76°

(15-11) Use circle O.

Given , what is ?

(A) 41°

(B) 82°

(C) 98°

(D) 164°

L

KJ

156°

3 6x

L

K

2 4x 166°J

J

K

L 15x

2 12x

J

K

L

120

5 15x


(16) 10.2 Solve problems involving angles, arcs, or sectors of circles.

(16-8) In circle J below,

What is the value of x?

(A) 78

(B) 54

(C) 50

(D) 27

(16-9) Use circle J below.


(A) 47

(B) 81

(C) 85

(D) 92

(16-10) Use circle J.


(A) 3

(B) 9

(C) 27

(D) 29

(16-11) Use circle J.


(A) 9

(B) 21

(C) 27

(D) 45

ZY

XW

LK

H

LM

K

N

J

H

LM

K

N

J


(17) 10.3 Solve problems involving arcs, chords, and radii of a circle.

(17-8) In , ,

, and .


(A) 20

(B) 54

(C) 131

(D) 350

(17-9) In , ,

, and .


(A) 16

(B) 24

(C) 48

(D) 62

(17-10) In circle N, ,

, and .


(A) 9

(B) 15

(C) 16

(D) 45

(17-11) In circle N, ,

, and

.


(A) 8.25

(B) 9.25

(C) 17

(D) 18

Q

A BP

C

D

R

L

M JH

K

N

L

M JH

K

N

L

M JH

K

N


(18) 10.3 Solve problems involving arcs, chords, and radii of a circle.

(18-8) In the figure below, and

,

What is ?

(A) 15

(B) 30

(C) 45

(D) 60


,

What is the ?

(A) 88

(B) 101

(C) 124

(D) 176


.

What is the ?

(A) 95°

(B) 130°

(C) 145°

(D) 175°


.

What is ?

(A) 31°

(B) 62°

(C) 64°

(D) 97°

PH

N

R

DA

C

B

DA

C

B

DA

C

B


(19) 10.4 Explore relationships among circles and external lines or rays.

(19-8) Two tangents are drawn from point P to circle H.

What conclusion is guaranteed by this diagram?

(A)

(B) ΔHNR is a right triangle.

(C) HNPR is a rhombus.

(D) HNPR is a kite.

(19-9) Two tangents are drawn from point D to circle A.


(A)

(B) ΔABC is a right triangle

(C) BC = BD

(D) ΔBCD is an isosceles triangle



(A) is a right triangle.

(B) is a right triangle.

(C) AD = CD

(D) BD = CD



(A) AD = BD

(B) AC = DC

(C)

(D) is a right triangle.

C

B

VD

W

T

U

A

10 cm

3 cm4 cm

N6 cm

H

G

EI

D

C

B

A

8 cm

2 cm3 cm

K

5 cm

3

5

M

A

Z

Y

X

JH

A

C

GE

B

D

F

x17

29

23

42


(20) 10.4 Explore relationships among circles and external lines or rays.

(20-8) All of the segments shown in the figure below are tangents to .

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

(20-9) All of the segments shown in the figure below are tangents to .

Given the measures in the figure above, what is the perimeter of quadrilateral AGHI?

(A) 18 cm

(B) 26 cm

(C) 31 cm

(D) 36 cm

(20-10) All segments shown in the figure below are tangent to circle A. M is the midpoint of .

Given the measures in the figure, what is the perimeter of ?

(A) 20 units

(B) 22 units

(C) 24 units

(D) 26 units

(20-11) Points B, D, F, and H are points of tangency to circle J. AB = 17, CE = 42,

EG = 23, and GA = 29.


(A) 14

(B) 17

(C) 25

(D) 31

R

N

A

W

S

C

K

E

G

C

H

D

F

A

D

U

V

WT

SR

C

Z

Y

XW

VU


(21) 10.5 Solve problems involving properties of circles using algebraic techniques.

(21-8) In , , ,

, and .

What is CN?

(A) 6

(B) 13

(C) 22

(D) 26

(21-9) In , , , and .


(A) –4

(B) –3

(C) 3

(D) 4

(21-10) In circle D, DS = DV, ST = 3x + 7, and UW = x + 4.


(A) –3

(B) −2.5

(C) −2

(D) −1.5

(21-11) In circle C, UW = XZ, VW = 2x + 14, and XY = 6x + 2.


(A) 5

(B) 4

(C) 3

(D) 2

K

C

O

LJ

S

M

TR

U

S

M

TR

U

Y

C

W

X Z


(22) 10.5 Solve problems involving properties of circles using algebraic techniques.

(22-8) is the diameter of ,

, and

.


(A)

(B)

(C) 4

(D) 6

(22-9) is the diameter of ,

,

,

and .


(A) 35

(B) 25

(C) 20

(D) 5

(22-10) is a diameter of circle M.

,

, and

.


(A) 20

(B) 34

(C) 41

(D) 45

(22-11) is a diameter of circle C.

,

, and

.


(A) 22

(B) 30

(C) 32.5


(D) 43.5

C'

B'

A'

A

B

C

B'

C'

A'

AC

B

C'

B'

A'

C

B

A

B

A

C

A′

B′

C′


(23) 11.1 Distinguish among the basic mapping functions: dilations, reflections, translations, and rotations.

(23-8) Determine the transformation that has mapped Δ to Δ .

(A) dilation

(B) reflection

(C) rotation

(D) translation

(23-9) Given the figure below:

What transformation mapped Δ

to Δ ?

(A) reflection

(B) rotation

(C) translation

(D) dilation

(23-10) Determine the transformation that has mapped to .

(A) dilation

(B) reflection

(C) rotation

(D) translation

(23-11) Determine the single transformation that has mapped to .

(A) translation

(B) rotation

(C) dilation

(D) reflection


(24) 11.4 Differentiate between examples of each type of symmetry.

(24-8) How many lines of symmetry does a square have?

(A) 0

(B) 1

(C) 2

(D) 4

(24-9) How many lines of symmetry does a rectangle have?

(A) 0

(B) 1

(C) 2

(D) 4

(24-10) How many lines of symmetry does an equilateral triangle have?

(A) 1

(B) 2

(C) 3

(D) 4

(24-11) How many lines of symmetry does a square have?

(A) 0

(B) 1

(C) 2

(D) 4

83

16

6

30°3

8

83


(25) 6.1 Differentiate between similar and congruent.

(25-8) Which figure contains two similar triangles that are not congruent?

(A)

(B)

(C)

(D)

(25-9) Which figure contains two congruent triangles?

(A)

(B)

(C)

(D)

(25-10) Which figure does NOT contain two similar triangles nor two congruent triangles?

(A)

(B)

(C)

(D)

(25-11) Which pair of figures is similar but NOT congruent?

(A)

(B)

(C)


(D)

Y

W X

Z 56

32

24

42D C

BA

Y

W X

Z 48

24

16

32D C

BA

6

3

8

4

NR

C WA

S

C 3

3

66

3D

E

A

BV

2

4

22

4

W

XY

Z


(26) 6.2 Determine scale ratios and write appropriate proportions.

(26-8) The following figures are similar.

What is the scale factor of WXYZ to ABCD?

(A) 1 to 2

(B) 3 to 1

(C) 3 to 2

(D) 4 to 3

(26-9) The following figures are similar.

What is the scale factor of WXYZ to ABCD?

(A) 3 to 2

(B) 3 to 1

(C) 4 to 3

(D) 1 to 2

(26-10) The figures below are similar.

What is the scale factor of to ?

(A) 3 to 8

(B) 1 to 2

(C) 2 to 3

(D) 3 to 4

(26-11) The figures below are similar.

What is the scale factor of ABCDE to VWXYZ?

(A) 3:2

(B) 3:6

(C) 4:2

(D) 4:3

(2x) in

(3x – 4) in

x

x + 10

6 3 in.x

4 7 in.x

60 cm

P = 400 cm

x


(27) 6.4 Solve proportion problems using algebraic techniques.

(27-8) 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) 8

(B) 12

(C) 16

(D) 24

(27-9) Two gardens are similar rectangles. Their scale factor is 3:1. The perimeter of the smaller garden is 40 feet. The lengths of the sides of the larger garden are represented by the variable expressions shown in the diagram below.


(A) 5

(B) 15

(C) 25

(D) 55

(27-10) Two windows are similar rectangles. Their scale factor is 5:6. The perimeter of the larger window is 240 inches. The length of the sides of the smaller window is represented by the variable expressions in the diagram.


(A) 9

(B) 11

(C) 19

(D) 23

(27-11) Two windows are similar rectangles. Their scale factor is 3:4. The width of the smaller window is 60 centimeters and the perimeter of the larger window is 400 centimeters.

What is the length x?

(A) 45 cm

(B) 80 cm

(C) 90 cm

(D) 100 cm



(28-8) The measures of the angles of a triangle have the ratio 4:6:7. What type of triangle is it?

(A) acute

(B) isosceles

(C) obtuse

(D) right


(A) obtuse

(B) isosceles

(C) acute

(D) right


(A) right

(B) acute

(C) obtuse

(D) not a triangle

(28-11) The measures of the angles of a triangle have the ratio 1:3:5. What is the measure of the largest angle?

(A) 50°

(B) 60°

(C) 90°

(D) 100°



(29-8) 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?

(A) 12 ft

(B) 32 ft

(C) 36 ft

(D) 90 ft

(29-9) The perimeter of a rectangle is 48 feet. The ratio of the width to the length is 1:5. What is the width of the rectangle?

(A) 4 ft

(B) 6 ft

(C) 8 ft

(D) 10 ft

(29-10) The perimeter of a rectangle is 300 feet. The ratio of the length to the width is 3:2. What is the length of the rectangle?

(A) 30 ft

(B) 90 ft

(C) 120 ft

(D) 150 ft

(29-11) A pipe that is 8 feet long is cut into two pieces whose lengths are in the ratio 1:3. What is the length of the longer piece?

(A) 3 ft

(B) 4 ft

(C) 6 ft

(D) 7 ft

15.6 m3 m

2 m

12 m3 m

2 m


(30) 6.5 Formulate and solve real world problems using similar triangles.

(30-8) 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?

(A) feet

(B) 25 feet

(C) feet

(D) 20 feet

(30-9) Mort measures the length of the shadow of a tree to be 35 feet long. At the same time his shadow measures 10 feet long and his height is 6 feet. How many feet tall is the tree?

(A) 58 ft

(B) 32 ft

(C) 21 ft

(D) 18 ft

(30-10) A student measures the height of a sign to be 2 meters. The shadow of the sign is 3 meters. The student notices that at the same time a nearby tree has a shadow of 15.6 meters.

How tall is the tree?

(A) 5.2 m

(B) 7.8 m

(C) 10.4 m

(D) 23.4 m

(30-11) A student notices that the shadows of a sign and a tree lie along the same line and end at the same point. The height of the sign is 2 meters and its shadow is 3 meters in length. The distance from the base of the sign to the base of the tree is 12 meters.

How tall is the tree?

(A) 8 m

(B) 10 m

(C) 11 m

(D) 14 m

15 m3 m

h

2 m

G

h

6 ft

11 ft2 ft

h

5 ft

12 ft3 ft

h

5 ft

32 ft8 ft


(31) 6.5 Formulate and solve real world problems using similar triangles.

(31-8) 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.

What is the height h of the flagpole in meters?

(A) 10 m

(B) 12 m

(C) 18 m

(D) 20 m

(31-9) Bernard places a mirror on the ground and then stands so that he can see the reflection of the top of a flagpole in the mirror.

What is the height h of the flagpole in feet?

(A) 12 ft

(B) 22 ft

(C) 33 ft

(D) 66 ft

(31-10) Matty places a mirror on flat ground, then stands so that the top of a nearby tree is visible in the mirror.

What is the height of the tree?

(A) 15 ft

(B) 20 ft

(C) 36 ft

(D) 60 ft

(31-11) As shown in the figure below, Jeremy places a mirror on flat ground, then stands so that the top of a nearby tree is visible in the mirror.

What is the height of the tree?

(A) 20 ft

(B) 29 ft

(C) 45 ft

(D) 51 ft

L

JH

BO

N

69

15

N

OP

JI

H

30°

70

U

WV

T

S

R

U

WV

T

S

R

56°


(32) 6.6 Prove that two triangles are similar.

(32-8) Given the two triangles pictured below.

What measure for would make ?

(A)

(B)

(C) 10

(D) 9

(32-9) Given the two triangles pictured below.


(A) 30°

(B) 60°

(C) 90°

(D) 120°

(32-10) Given the triangles pictured.


(A) 35°

(B) 55°

(C) 70°

(D) 110°

(32-11) Use the figures below.


(A) 34°

(B) 56°

(C) 68°

(D) 112°

A

D

CB

10.5

7

z

4

X

Z

WY

6

a

4

3

STQ

R

y

36

7

9

STQ

R

6

w

3

4


(33) 6.7 The student will explore properties of proportionality within a triangle.

(33-8) In the triangle below,

What is the value of z?

(A) 6

(B) 12

(C) 13.5

(D) 21.5

(33-9) In the triangle below, .

What is the value of a?

(A) 2

(B) 2.5

(C) 4

(D) 4.5

(33-10) In triangle QRS, bisects .

What is the value of y?

(A)

(B)

(C) 14

(D) 28

(33-11) In triangle QRS, bisects .

What is the value of w?

(A) 7

(B) 8

(C) 9

(D) 12

S

H

T

R

M x

6

415

Q

R

G

J

P

x9

68

15 x

10

15

PG

J

R

Q

6 12

x

9

PG

J

R

Q


(34) 6.7 The student will explore properties of proportionality within a triangle.



(A) 9

(B) 10

(C)

(D)



(A) 11

(B) 12

(C) 18

(D) 20

(34-10) In triangle PQR, .


(A) 5

(B) 6

(C) 10

(D) 30

(34-11) In triangle PQR, .


(A) 3

(B) 6

(C) 15

(D) 18


(35) 7.2 Explore geometric mean relationships within a right triangle.

(35-8) What is the geometric mean of 16 and 36?

(A) 9

(B) 10

(C) 24

(D) 26


(A) 14

(B) 15

(C) 16

(D) 17

(35-10) What is the geometric mean of and 400?

(A)

(B)

(C) 10

(D) 20


(A) 8

(B) 10

(C)

(D)

21 ft

28 ft

D

C

B

A

15 ft

20 ft

D

C

B

A

24 ft

10 ft

D C

BA

12 yd

5 yd

D C

BA


(36) 7.3 Solve problems using the Pythagorean Theorem.

(36-8) Nan stands at the corner of the rectangular driveway shown below.

How far must Nan walk diagonally across the driveway (A to B)?

(A) 7 ft

(B) 14 ft

(C) 35 ft

(D) 49 ft

(36-9) Gina stands at the corner of the rectangular garden shown below.

How much shorter in feet is it to walk diagonally through the garden (A to B) instead of walking around its edge (A to C and C to B)?

(A) 5 ft

(B) 10 ft

(C) 15 ft

(D) 25 ft

(36-10) Fred stands at corner A of a rectangular field. He wants to walk to opposite corner C.

How much farther is it to walk from A to C along the edge of the field than to walk diagonally across the field?

(A) 8 ft

(B) 14 ft

(C) 26 ft

(D) 34 ft

(36-11) Fred stands at corner A of a rectangular field. He wants to walk to the opposite corner C.

What is the shortest distance from A to C?

(A) 7 yd

(B) 12 yd

(C) 13 yd

(D) 17 yd

B

A

24 in.

8 in.6 in.

B

A 12 cm

3 cm

4 cm

B

A 15 cm

10 cm

5 cm

B

A 12 cm

20 cm

9 cm



(37-8) A box is shown below.

What is AB?

(A) 26 in.

(B) 38 in.

(C) in.

(D) in.

(37-9) Use the dimensions given in the diagram below.

What is the length of the diagonal from A to B?

(A) cm

(B) cm

(C) 5 cm

(D) 13 cm

(37-10) A rectangular prism has dimensions as shown.


(A) 20 cm

(B) cm

(C) 30 cm

(D) cm

(37-11) A rectangular prism has dimensions as shown.


(A) 14 cm

(B) 25 cm

(C) 32 cm

(D) 41 cm

x16

135

x15

106

1715

x6

2016

13x





(A) 12

(B) 20

(C) 22

(D) 30



(A) 25

(B) 21

(C) 17

(D) 8



(A) 6.8

(B) 8

(C) 10

(D) 23.6



(A) 3

(B) 5

(C) 12

(D) 17


(39) 7.4 Solve problems using the converse of the Pythagorean Theorem and related theorems for obtuse or acute triangles.

(39-8) The three sides of a triangle are

centimeters, centimeters, and centimeters. What is the best description for this triangle?

(A) acute triangle

(B) equiangular triangle

(C) obtuse triangle

(D) right triangle

(39-9) The three sides of a triangle are 5 cm, 6 cm, and 10 cm. What is the best description for this triangle?

(A) obtuse triangle

(B) equiangular triangle

(C) acute triangle

(D) right triangle

(39-10) The three sides of a triangle are 13 meters, 5 meters and 12 meters. What is the best description for this triangle?

(A) acute

(B) equiangular

(C) obtuse

(D) right

(39-11) The three sides of a triangle are

inches, inches, and inches. Which is a classification for this triangle?

(A) acute

(B) obtuse

(C) right

(D) scalene

d

45°

7 mi

18 ft60° H

S

50 ft

60°

d

60°

d12 3

60°


(40) 7.4 Solve problems using the converse of the Pythagorean Theorem and related theorems for obtuse or acute triangles.

(40-8) A jet is flying 7 miles above the ground. The pilot spots an airport as shown below.

What is the distance d from the plane to the airport?

(A) mi

(B) mi

(C) 7 mi

(D) 14 mi

(40-9) A seagull in a palm tree spots a hot dog on the beach.

How far is the seagull from the hot dog?

(A) 9 ft

(B) ft

(C) ft

(D) 36 ft

(40-10) Use the triangle below.

What is the length of d?

(A) 25 ft

(B) ft

(C) ft

(D) 100 ft

(40-11) Use the triangle below.

What is the value of d ?

(A) 12

(B) 24

(C)

(D)

30°

4

45°y

30°

y

45°

16

y

45º

30º

4 3

y4 2

30º45°


(41) 7.5 Solve problems utilizing the ratios of the sides of special right triangles.



(A)

(B)

(C)

(D)



(A)

(B)

(C) 8

(D) 16

(41-10) Use the dimensions given in the diagram.


(A)

(B) 6

(C)

(D) 12



(A) 4

(B)

(C)

(D) 8

52 m



(42-8) In rectangle ABCD, BD = 12 and . What is the length of

the longer side of the rectangle?

(A) 6

(B) 12

(C)

(D)

(42-9) A square has a diagonal length of

inches. What is the length in inches of a side?

(A) in

(B) 6 in.

(C) in.

(D) 12 in.

(42-10) A square has diagonal length of meters. What is the length of the side of the square?

(A) 7 m

(B) 14 m

(C) m

(D) m

(42-11) The square below has diagonal length

of meters.

What is the length of a side?

(A) 5 m

(B) 10 m

(C) m

(D) m

10

r

50°

r

10

40°

r

10

20°

1000

10°

r


(43) 7.6 Define and apply basic trigonometric ratios of sine, cosine, and tangent.

(43-8) Use the table and the dimensions given in the diagram below.

sin cos tan 20° .3420 .9397 .364030° .5000 .8660 .577440° .6428 .7660 .839150° .7660 .6428 1.1918

What is the value of r?

(A) 11.918

(B) 8.391

(C) 7.660

(D) 6.428


sin cos tan 20° .3420 .9397 .364030° .5000 .8660 .577440° .6428 .7660 .839150° .7660 .6428 1.1918


(A) 6.428

(B) 7.660

(C) 8.391

(D) 11.918

(43-10) Use the table and the dimensions given in the diagram.

sin cos tan 20° .3420 .9397 .364030° .5000 .8660 .577440° .6428 .7660 .839150° .7660 .6428 1.1918


(A) 3.42

(B) 3.64

(C) 8.66

(D) 9.40

(43-11) Use the table and the dimensions given in the diagram.

sin cos tan 10° .1736 .9848 .176320° .3420 .9397 .364030° .5000 .8660 .577440° .6428 .7600 .8391

What is the approximate value of r?

(A) 174

(B) 342

(C) 500

(D) 985

15 9

12 C

B

A

106

8 C

B

A

257

24 C

B

A

135

12 C

B

A



(44-8) Use the dimensions given in the right triangle below.

What is the cosine of ?

(A)

(B)

(C)

(D)


What is the tangent of ?

(A)

(B)

(C)

(D)


What is the sine of

(A)

(B)

(C)

(D)


What is the tangent of ?

(A)

(B)

(C)

(D)

Angle of descent

10 mi3.4 mi

Angle of descent

10 miles

9.4 miles

Angle of descent

10 miles

3.6 miles

100 ft64 ft


(45) 7.7 Solve problems using the trigonometric


sin cos tan 20° .3420 .9397 .364030° .5000 .8660 .577440° .6428 .7660 .839150° .7660 .6428 1.1918

What is the approximate angle of descent?

(A) 50°

(B) 40°

(C) 30°

(D) 20°


sin cos tan 20° .3420 .9397 .364030° .5000 .8660 .577440° .6428 .7660 .839150° .7660 .6428 1.1918

What is the airplane’s approximate angle of descent?

(A) 20°

(B) 30°

(C) 40°

(D) 50°


sin cos tan 20° .3420 .9397 .364030° .5000 .8660 .577440° .6428 .7660 .839150° .7660 .6428 1.1918

What is the airplane’s approximate angle of descent?

(A) 20°

(B) 30°

(C) 40°

(D) 50°


sin cos tan 10° .1736 .9848 .176320° .3420 .9397 .364030° .5000 .8660 .577440° .6428 .7600 .8391

What is the kite’s approximate angle of elevation?

(A) 10°

(B) 20°

(C) 30°

(D) 40°

53°

150 ft

h

47°

d120

A

57°q

65A

B

C

50°75

A

B

C

x


(46) 7.7 Solve problems using the trigonometric ratios.


Which equation would be used to find the distance h from the hot air balloon to the ground?

(A)

(B)

(C)

(D)


Which equation would be used to find the distance d from the hot air balloon to point A on the ground?

(A)

(B)

(C)

(D)


Which equation would be used to find the distance q from point A to point B?

(A)

(B)

(C)

(D)


Which equation would be used to find the length of x?

(A)

(B)

(C)

(D)

d128 ft

40°

100 fth

50°

100 ft

30°d

30º

100 yd

h


(47) 7.7 Solve problems using the trigonometric ratios.


sin cos tan

20° .3420 .9397 .364030° .5000 .8660 .577440° .6428 .7660 .839150° .7660 .6428 1.1918

What is the approximate length d of the kite string?

(A) 256 ft

(B) 200 ft

(C) 168 ft

(D) 100 ft


sin cos tan 20° .3420 .9397 .364030° .5000 .8660 .577440° .6428 .7660 .839150° .7660 .6428 1.1918

What is the approximate height h of the kite off the ground in feet?

(A) 50 feet

(B) 64 feet

(C) 77 feet

(D) 120 feet


sin cos tan 20° .3420 .9397 .364030° .5000 .8660 .577440° .6428 .7660 .839150° .7660 .6428 1.1918

What is the approximate ground distance d in feet?

(A) 77 ft

(B) 87 ft

(C) 93 ft

(D) 115 ft


sin cos tan 10° .1736 .9848 .176320° .3420 .9397 .364030° .5000 .8660 .577440° .6428 .7600 .8391

What is the approximate height h of the structure?

(A) 50 yd

(B) 58 yd

(C) 83 yd

(D) 87 yd

10

3 7x

2x – 6

C

A

DB

8

3

2xA

C

D

B

13

5

A

C

D

B

15

8

A

C

D

B


(48) 10.6 Solve problems involving secant segments and tangent segments for a circle.

(48-8) In circle D below, is tangent to

at A, and is tangent to at C.

What is the length of ?

(A) 14

(B) 15

(C) 24

(D) 26

(48-9) In the figure below, is tangent to

at A and is tangent to at C.

Find the value of x.

(A) 2

(B) 3

(C) 4

(D) 5

(48-10) In the figure, is tangent to circle

D at A, and is tangent to circle D at C.

What is the value of BC?

(A) 3

(B) 5

(C) 12

(D) 13

(48-11) In circle D, is tangent at A, and

is tangent at C.


(A) 23

(B) 17

(C) 16

(D) 15

5x

6

2 5 1x A

C

D

B

7

6x – 12

3x + 6

P

N

DM

10

4x – 5

2x + 5

N

P

DM

12

6x – 12

3x + 6

A

C

DB




at A and is tangent to at C.


(A) 2

(B) 3

(C) 4

(D) 5

(49-9) In circle D below, is tangent to at N and is tangent to

at P.


(A) 25

(B) 24

(C) 7

(D) 6

(49-10) In circle D, is tangent to circle D at N and is tangent to circle D at P.


(A) 12

(B) 15

(C) 20

(D) 24

(49-11) In circle D, is tangent at A, and

is tangent at C.


(A) 2

(B) 4

(C) 6

(D) 12

8 cm

x

6 cmV

R

S

P

x

10 cm

5 cmC

A

D

B

21 m

x

4 mC

A

D

B

20 m

3 mD

E

CB

x

4 mA




the circle at R and is a secant.


(A) 48 cm

(B) 84 cm

(C) cm

(D) cm

(50-9) In the figure below, is tangent to the circle at A and is a secant.


(A) 2 cm

(B) 5 cm

(C) 15 cm

(D) 25 cm

(50-10) In the figure below, is tangent to the circle at A and is a secant.


(A) 9 m

(B) 10 m

(C) 25 m

(D) 100 m

(50-11) In the figure below, and are secants of the circle.

What is DE?

(A) 15 m

(B) 18 m

(C) 29 m

(D) 32 m

Geometry Semester II Exam CompilationFree Response

2008–2011(51) 6.6 Prove that two triangles are similar.

(51-8) Given with right angle at C and altitude , draw the picture and explain why .

(51-9) Given trapezoid TRQP with parallel sides and . Diagonals and intersect at point Z. Draw the picture and explain why .

(51-10) Given with altitude and right angle C, make a diagram and explain why

(51-11) Given kite ABCD with and . The diagonals intersect at point E. Draw a diagram and explain why .


2008–2011(52) 7.7 Solve problems utilizing the ratios of the sides of special right triangles.

(52-8) Find the length of the altitude of an isosceles triangle with vertex angle 120 and base length of 30 centimeters. Give answer in simplified radical form.

(52-9) The diagonal of a square divides it into two 45-45-90 triangles. The diagonal has length 10 centimeters. Find the area of the square.

(52-10) The diagonal of a rectangle divides it into two 30º-60º-90º triangles. The diagonal has a length of 16 inches. What is the area of the rectangle? (Give the answer in simplest radical form.)

(52-11) The diagonal of a square has length . What is the area of the square.


2008–2011(53) 8.2 Solve problems using perimeters or areas of geometric figures.

(53-8) Find the area of a regular hexagon with an apothem of 9 centimeters. Give answer in simplified radical form.

(53-9) Find the area of a regular hexagon with a side of 6 centimeters. Give the answer in simplified radical form.

(53-10) What is the area of a regular hexagon with a radius of 8 cm? (Give the answer in simplest radical form.)

(53-11) Compute the area of a regular hexagon with an apothem of . Give the answer in simplest radical form

H

EI

F

J

G

K

Geometry Honors Semester II Exam Compilation2008–2011

(1) 8.4 Solve problems involving geometric probability.

(1-8) The figure below is a regular hexagon with a side length of 8 centimeters.

What is the probability that a randomly thrown dart will land in the shaded region?

(A)

(B)

(C)

(D)

(1-9) The figure below is a regular hexagon with a radius of 6 centimeters.

What is the probability that a randomly thrown dart hitting the figure will land in the shaded region?

(A)

(B)

(C)

(D)

(1-10) The figure is a regular triangle.


(A)

(B)

(C)

(D)

(1-11) In are midpoints.

If GI = 36, what is KG?

(A) 6

(B) 12

(C) 18

(D) 24

555

TS

RQP

70°

55°

55° 65° 55°

80°40°

60°

60°


(2) 8.4 Solve problems involving geometric probability.

(2-8) The concentric circles below have radii of 4 centimeters, 10 centimeters, and 18 centimeters.

What is the probability that a randomly thrown dart will land in the white region, assuming it hits the board?

(A)

(B)

(C)

(D)

(2-9) The concentric circles below have radii of 2 centimeters, 5 centimeters, and 9 centimeters.


(A)

(B)

(C)

(D)

(2-10) What is the probability that a randomly thrown dart hitting the figure will land in the shaded region?

(A)

(B)

(C)

(D)

(2-11) Based on the dimensions given in the diagram, what is the longest line segment in the diagram?

(A)

(B)

(C)


(D)

16 cm

12 cm

18 cm



(3-8) In the square below, all adjacent circles are congruent, externally tangent to each other, and outer circles are tangent to the square.

What is the area of the unshaded region?

(A) cm2

(B) cm2

(C) cm2

(D) cm2


What is the area of the shaded region in square centimeters?

(A) (144 − 4π) cm2

(B) (144 − 16π) cm2

(C) (144 − 36π) cm2

(D) (144 − 144π) cm2


What is the area of the shaded region?

(A) cm2

(B) cm2

(C) cm2

(D) cm2

(3-11) has an endpoint at U , and the

midpoint is at M . What are the coordinates of endpoint V?

(A)

(B)

(C)

(D)

3 cm

4 cm

3 cm

5 cm

5 cm

9 cm


(4) 9.2 Solve problems involving surface areas and volumes of various geometric solids.

(4-8) A snow cone consisting of a cone and a half-sphere is shown below. The base of the cone is a great circle on the sphere.

(surface area formulas given)

What is the surface area of the three-dimensional object in square centimeters?

(A) 30π cm2

(B) 33π cm2

(C) 39π cm2

(D) 42π cm2

(4-9) A snow cone consisting of a cone and a half-sphere is shown below. The base of the cone is a great circle on the sphere.

(surface area formulas given)

What is the volume of the snow cone in cubic centimeters?

(A) cm3

(B) cm3

(C) cm3

(D) cm3

(4-10) A snow cone consists of a cone and a hemisphere. The radius of the cone is the same as the radius of the hemisphere.

What is the volume of the snow cone?

(A) cm3

(B) cm3

(C) cm3

(D) cm3

(4-11) Rectangle MHRG has vertices

, , , and

. What is the length of diagonal ?

(A)

(B)


(C)

(D)

14 in.

2 in.

9 in.

6 in.18 in.

8 cm

2 cm

10 cm

5 cm12 cm

2 in.

D

BCA

AC = 1 in.34



(5-8) A glass block is in the shape of a rectangular prism. It has a hole passing through it also in the shape of a rectangular prism.

What is the volume of glass needed in cubic inches?

(A) 80 in3

(B) 252 in3

(C) 720 in3

(D) 972 in3

(5-9) A cinder block is in the shape of a rectangular prism. It has a hole passing through it also in the shape of a rectangular prism.

What is the volume of material needed in cubic centimeters?

(A) 160 cm3

(B) 440 cm3

(C) 600 cm3

(D) 760 cm3

(5-10) A 2-inch piece of plastic pipe is in the shape of a cylinder with a cylindrical hole passing through it. The outside diameter is one inch; the inside

diameter is inches.

What is the volume of the plastic material?

(A) in3

(B) in3

(C) in3

(D) in3

(5-11) In an indirect proof, after assuming the opposite of the “Proof Statement” (conclusion), the next step in the process is to

(A) find a contradiction

(B) prove the false assumption

(C) prove the given information

(D) use CPCTC

135°

15

10

60°12 cm

8 cm

120º

13 ft

7 ft



(6-8) Use the dimensions given in the diagram of an isosceles trapezoid below.

What is the area of the trapezoid?

(A)

(B)

(C)

(D)

(6-9) Use the dimensions given in the diagram of an isosceles trapezoid below.

What is the area of the trapezoid in square centimeters?

(A) cm2

(B) cm2

(C) 20 cm2

(D) 40 cm2

(6-10) Use the dimensions given in the diagram of an isosceles trapezoid.

What is the area of the trapezoid?

(A) 30 ft2

(B) ft2

(C) ft2

(D) 60 ft2

(6-11) To begin an indirect proof, an initial assumption is made. If one were trying to prove that x = 9, what should be the initial assumption?

(A) x = 9

(B) x < 9

(C) x > 9

(D)



(7-8) Given a 30°-60°-90° triangle, what is the cosine of the 60° angle?

(A)

(B)

(C)

(D)

(7-9) Given a 30°-60°-90° triangle, what is the tangent of the 30° angle?

(A)

(B)

(C)

(D)

(7-10) Given a 45º-45º-90º triangle, what is the sine of the 45º angle?

(A)

(B)

(C) 1

(D)

(7-11) In the diagram, which coordinates would result in a kite?

5 10

5

10

x

y

(A)

(B)

(C)

(D)


(8) 10.8 Graph a circle and determine its equation.

(8-8) A circle with a point is

centered at . What is the equation of the circle?

(A)

(B)

(C)

(D)

(8-9) A circle with a radius of 4 is centered

at . What is the equation of the circle?

(A)

(B)

(C)

(D)

(8-10) A circle with radius of 5 is centered at

the point . What is the equation of the circle?

(A)

(B)

(C)

(D)

(8-11) The nth term of a sequence is . If the value of a term is 400, what is the next term?

(A) 8

(B) 289

(C) 409

(D) 529

2 ft

10 ft

16 ft

4 ft4 ft

4 ft

2 ft

10 ft

16 ft

4 ft4 ft

4 ft

2 ft

12 ft

16 ft

4 ft4 ft

4 ft



(9-8) The room shown below is to have crown molding installed around the ceiling’s perimeter.

Approximately how many feet of molding are needed to complete the room?

(A) 40 ft

(B) 52 ft

(C) 54 ft

(D) 60 ft

(9-9) The room shown below is to be carpeted. Carpet is sold by the square yard.

What is the minimum number of square yards needed to carpet the room?

(A) 20 yd2

(B) 40 yd2

(C) 54 yd2

(D) 58 yd2

(9-10) The room shown below is to be tiled.

What is the area of the room?

(A) 192 ft2

(B) 200 ft2

(C) 204 ft2

(D) 216 ft2

(9-11) Given points and , what is a possible value of x if the length of is 13?

(A) –5

(B) –1

(C) 5

(D) 12

100 ft

d

50°

30°

100 ft

d

50°

40°

200 ft

d

50°

30°


(10) 7.8 Solve problems using trigonometric ratios.

(10-8) A lighthouse keeper spots a boat moving away from the lighthouse, first at 30° and then at 50°. The height of the light house shown below is 100 feet above sea level.

What is the approximate distance d the boat traveled?

(A) 22 ft

(B) 61 ft

(C) 72 ft

(D) 89 ft

(10-9) An air traffic controller spots a taxiing aircraft, first at 50° and then at 40°. The height of the control tower shown below is 100 feet.

What is the approximate distance d the aircraft traveled?

(A) 10 ft

(B) 18 ft

(C) 23 ft

(D) 36 ft

(10-10) An air traffic controller spots a taxiing aircraft, first at 50º and then at 30º. The height of the control tower shown below is 200 feet.

What is the approximate distance d that the aircraft taxied?

(A) 20 ft

(B) 45 ft

(C) 53 ft

(D) 123 ft

(10-11) In isosceles triangle HMS, is the

vertex angle. If

and , what is ?

(A) 10°

(B) 22°

(C) 79°

(D) 80°

sin cos tan 20° .3420 .9397 .364030° .5000 .8660 .577440° .6428 .7660 .839150° .7660 .6428 1.1918

sin cos tan 20° .3420 .9397 .364030° .5000 .8660 .577440° .6428 .7660 .839150° .7660 .6428 1.1918

sin cos tan 20° .3420 .9397 .364030° .5000 .8660 .577440° .6428 .7660 .839150° .7660 .6428 1.1918

Obsolete Geometry Semester 2 Exam Compilation 2008-2011

(1) 6.6 Prove that two triangles are similar.

(1-8) Given with right angle at C and altitude , draw the picture and prove .

(1-9) Given trapezoid TRQP with parallel sides and . Diagonals and intersect at point Z. Draw the picture and explain why .

(1-10) Given with altitude and right angle C, by the Right Triangle Similarity Theorem. Prove the Right Triangle Similarity Theorem.

(1-11) Given kite ABCD with and . The diagonals intersect at point E. Prove .



(2-8) Find the length of the altitude of an isosceles triangle with vertex angle 120 and a base length of x centimeters. Give answer in simplified radical form in terms of x.

(2-9) The diagonal of a square divides it into two 45-45-90 triangles. The diagonal has length d. Find the area of the square in terms of d.

(2-10) The two diagonals of a square divide it into four 45º-45º-90º triangles. The legs of these triangles have length l. What is the area of the square in terms of l?

(2-11) The diagonal of a square has length d. Express the area of the square in terms of d.



(3-8) Explain how to find the area of a regular hexagon if only the length of the apothem is known.

(3-9) Explain how to find the area of a regular hexagon if only the length of a side is known.

(3-10) Explain how to find the area of a regular hexagon if the only length of the radius is known.

(3-11) Explain how to determine the area of a regular hexagon if only the length of its apothem is known.

obsolete geometry semester 2 exam compilation...

Documents