Geometry H 2008 2009 Semester 2 Assessment Released

Geometry H 2008–2009 Semester 2 Assessment — Released Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 4. BEGIN PART I (50 questions)

1. 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

2. In the figure below, the adjacent sides of the polygon are perpendicular.

What is the perimeter of the figure?

A. 58 B. 77 C. 80 D. 91

3. 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

2008–2009 1 GO ON Clark County School District Revised 07/22/2009 Geometry H 2008–2009 Semester 2 Assessment — Released Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT

5. 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

6. Given the figure below, V

A D H F

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

A. base edge B. height C. lateral edge D. slant height

7. 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

8. A square pyramid has height of 4 inches and the measure of the base 10. A cone has a height of 9 inches and a edge is 6 inches. radius of 3 inches.

1 1 Volume =  (Area of Base)  height Volume =  (Area of Base)  height 3 3

4 in. 9 in.

6 in. 3 in. What is the volume of the pyramid? What is the volume of the cone in terms 3 A. 16 in. of ? B. 48 in.3 A. 108π in.3 C. 96 in.3 B. 81π in.3 D. 144 in.3 C. 27π in.3 9. D. 18π in.3

11. 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 in.2 B. 50 in.2 C. 85 in.2

2008–2009 4 GO ON Clark County School District Revised 07/22/2009 Geometry H 2008–2009 Semester 2 Assessment — Released Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT D. 250 in.2

12. A cereal box is 10 inches by 2 inches by 15. A pizza parlor has two different sizes of 15 inches. After breakfast, the box is pizza. The smaller one has a diameter half full. of 10 inches and the larger one has a diameter of 18 inches.

What is the ratio of their areas?

A. 5 :3 B. 10 : 3 2 C. 5: 9 D. 25:81 How many cubic inches of cereal are left inside? 16. Which accurately describes a secant?

A. 75 in.3 A. A line that intersects a circle at two points. B. 150 in.3 B. A segment whose endpoints are on the C. 300 in.3 circle. D. 600 in.3 C. A segment having an endpoint on the circle and an endpoint at the center of the circle. 13. Two similar rectangular prisms have a scale factor of 3:1. The larger prism has D. A line that intersects a circle at exactly one a volume of 135 cubic centimeters. point.

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

A. 5 cm3 B. 15 cm3 C. 25 cm3 D. 45 cm3

2008–2009 6 GO ON Clark County School District Revised 07/22/2009 Geometry H 2008–2009 Semester 2 Assessment — Released Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 19. 17. Use the figure below.

E C G B

Which represents a chord?

A. CA B. BC C. AD D. AG

18. Use circle O below.

Q 86°

Since m� PQR 86 , what is the measure of PTR ?

A. 43° B. 86° C. 90° D. 172°

2008–2009 7 GO ON Clark County School District Revised 07/22/2009 Geometry H 2008–2009 Semester 2 Assessment — Released Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT D. 62 20. Use circle J below.

(2x - 4) J 166°

What is the value of x?

A. 47 B. 81 C. 85 D. 92

21. In e P , mRS=(2 x + 9) , mTU=( x + 7) , and m� RQS 32 .

A. 16 B. 24 C. 48

22. In the figure below, m� H 13 and 25. All of the segments shown in the figure mMN = 150 , below are tangents toe K .

W G M J 5 cm C A H L 8 cm K

K D B 3 cm 2 cm

N I E H hat is the mJK ? Given the measures in the figure above, A. 88 what is the perimeter of quadrilateral AGHI? B. 101 A. 18 cm C. 124 B. 26 cm D. 176 C. 31 cm 23. Two tangents are drawn from point D to D. 36 cm circle A. 26. In e A , CD@ FE , CH=4 x + 2 , and C FE=6 x + 10 .

E G A D F C A What conclusionB is guaranteed by this H diagram?

1 D A. mBC= m BDC 2 What is the value of x? B. ΔABC is a right triangle C. BC = BD A. –4 D. ΔBCD is an isosceles triangle B. –3 C. 3 24.

2008–2009 9 GO ON Clark County School District Revised 07/22/2009 Geometry H 2008–2009 Semester 2 Assessment — Released Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT D. 4 28. SR is the diameter of e M , 27. m� RMT+ ( x 15) , m� UMR+ (3 x 15) , and m� SMT- (4 x 10) .

A. 35 B. 25 C. 20 D. 5

29. Given the figure below:

What transformation mapped Δ ABC to Δ Aⅱ B C ?

A. reflection B. rotation C. translation

2008–2009 10 GO ON Clark County School District Revised 07/22/2009 Geometry H 2008–2009 Semester 2 Assessment — Released Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT D. dilation 31. How many lines of symmetry does a 30. rectangle have?

A. 0 B. 1 C. 2 D. 4

32. Which figure contains two congruent triangles?

2008–2009 11 GO ON Clark County School District Revised 07/22/2009 Geometry H 2008–2009 Semester 2 Assessment — Released Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 35. 33. The following figures are similar.

Z 48 Y

D 32 C

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

34. 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.

x + 10

A. 5 B. 15 C. 25 D. 55

36. The measures of the angles of a triangle have the ratio 2:3:7. What type of triangle is it?

A. obtuse B. isosceles C. acute D. right

37. 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

38. 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

39. Bernard places a mirror on the ground 41. Given the two triangles pictured below. and then stands so that he can see the reflection of the top of a flagpole in the H P O mirror.

N 30° I J

What measure for N would make DHIJ: D NOP ?

A. 30° h B. 60° C. 90° D. 120°

6 ft 42. In the triangle below, 蠤YXW ZXW . Y 2 ft 11 ft 3 W 4 What is the height h of the flagpole in Z feet? a A. 12 ft 6 B. 22 ft C. 33 ft X D. 66 ft

40. What is the value of a?

A. 2 B. 2.5 C. 4 D. 4.5

43. In the triangle below, JGP RQ . 46. Gina stands at the corner of the rectangular garden shown below. P G D B 6 Q 8 J x 15 ft 9

R A 20 ft C

What is the value of x? How much shorter in feet is it to walk A. 11 diagonally through the garden (A to B) instead of walking around its edge (A to B. 12 C and C to B)? C. 18 A. 5 ft D. 20 B. 10 ft 44. What is the geometric mean of 9 and 25? C. 15 ft D. 25 ft A. 14 B. 15 47. Use the dimensions given in the diagram C. 16 below. D. 17 B 4 cm 45. 3 cm

A 12 cm

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

A. 4 10 cm B. 155 cm C. 5 cm D. 13 cm

48. Use the dimensions given in the diagram 51. A seagull in a palm tree spots a hot dog below. on the beach.

S 6 10

60° H 18 ft What is the value of x? How far is the seagull from the hot dog? A. 25 A. 9 ft B. 21 B. 18 2 ft C. 17 D. 8 C. 18 3 ft D. 36 ft 49. The three sides of a triangle are 5 cm, 6 cm, and 10 cm. What is the best 52. Use the dimensions given in the diagram description for this triangle? below. A. obtuse triangle 16 B. equiangular triangle y C. acute triangle 45° 30° D. right triangle What is the value of y? 50. A. 8 2 B. 8 3 C. 8 D. 16

53. A square has a diagonal length of 12 2 56. Use the dimensions given in the right inches. What is the length in inches of a triangle below. side? B A. 3 2 in. 10 B. 6 in. 6 C. 6 2 in. A C D. 12 in. 8 What is the tangent of A ? 54. Use the table and the dimensions given in the diagram below. 8 A. 10 8 B. r 6 6 40° C. 10 10 6 q D. sin  cos  tan  8 20° .3420 .9397 .3640 30° .5000 .8660 .5774 40° .6428 .7660 .8391 50° .7660 .6428 1.1918

What is the value of r?

A. 6.428 B. 7.660 C. 8.391 D. 11.918

2008–2009 17 GO ON Clark County School District Revised 07/22/2009 Geometry H 2008–2009 Semester 2 Assessment — Released Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 120 D. d = 57. Use the table and the dimensions given sin 47 in the diagram below. 59. Angle of descent

10 miles

9.4 miles

q sin  cos  tan  20° .3420 .9397 .3640 30° .5000 .8660 .5774 40° .6428 .7660 .8391 50° .7660 .6428 1.1918

What is the airplane’s approximate angle of descent?

A. 20° B. 30° C. 40° D. 50°

58. Use the dimensions given in the diagram below.

d 120 47° A

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

A. d =120 tan 47 B. d =120sin 47 120 C. d = tan 47

60. Use the table and the dimensions given in the diagram below.

100 ft h

q sin  cos  tan  20° .3420 .9397 .3640 30° .5000 .8660 .5774 40° .6428 .7660 .8391 50° .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

2008–2009 19 GO ON Clark County School District Revised 07/22/2009 Geometry H 2008–2009 Semester 2 Assessment — Released Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT 63. 61. In the figure below, AB is tangent to e D at A and CB is tangent to e D at C.

A 2x B 3

Find the value of x.

A. 2 B. 3 C. 4 D. 5

62. In circle D below, MN is tangent to e D at N and MP is tangent to e D at P.

3x + 6 7 M D

6x – 12 P

What is the length of MP ?

A. 25 B. 24 C. 7 D. 6

64. In the figure below, AB is tangent to the circle at A and BD is a secant.

A 10 cm B

5 cm C x D

A. 2 cm B. 5 cm C. 15 cm D. 25 cm

END PART I

GO ON TO PART II

BEGIN PART II (10 questions) 67. The concentric circles below have radii of 2 centimeters, 5 centimeters, and 9 centimeters. 65. 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 What is the probability that a randomly in the shaded region? thrown dart hitting the figure will land in the shaded region? 1 A. 16 3 A. 256 1 B. 7 2 B. 27 2 C. 81 3 C. 256 3 D. 20 4 D. 27 66.

68. 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 shaded region in square centimeters?

A. (144 − 4π) cm2 B. (144 − 16π) cm2 C. (144 − 36π) cm2 D. (144 − 144π) cm2

69. 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.

1 Volume of a cone =  (Area of Base)  height 3

4 Volume of a sphere =  π  (radius of a Great Circle)3 3

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

A. 30p cm3

2008–2009 23 GO ON Clark County School District Revised 07/22/2009 Geometry H 2008–2009 Semester 2 Assessment — Released Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT B. 48p cm3 C. 54p cm3 D. 72p cm3

70. A cinder block is in the shape of a 73. Given a 30°-60°-90° triangle, what is the rectangular prism. It has a hole passing tangent of the 30° angle? through it also in the shape of a rectangular prism. 1 A. 2 2 cm B. 3 10 cm 8 cm 3 C. 2 3 5 cm D. 12 cm 3 What is the volume of material needed in cubic centimeters? 74. A circle with a radius of 4 is centered at (3,- 2) . What is the equation of the A. 160 cm3 circle? B. 440 cm3 2 2 A. x-3 + y + 2 = 4 C. 600 cm3 ( ) ( ) 2 2 D. 760 cm3 B. ( x+3) +( y - 2) = 4

2 2 71. Use the dimensions given in the diagram C. ( x-3) +( y + 2) = 16

of an isosceles trapezoid below. 2 2 D. ( x+3) +( y - 2) = 16 8 cm

60° 12 cm

What is the area of the trapezoid in square centimeters?

A. 20 3 cm2 B. 40 3 cm2 C. 20 cm2 D. 40 cm2

75. The room shown below is to be carpeted. Carpet is sold by the square yard.

4 ft 4 ft 2 ft 4 ft

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

76. 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.

 sin  cos  tan  20° .3420 .9397 .3640 30° .5000 .8660 .5774 40° 40° .6428 .7660 .8391 50° .7660 .6428 1.1918 50° 100 ft

2008–2009 26 Clark County School District Revised 07/22/2009 Geometry H 2008–2009 Semester 2 Assessment — Released Note: Diagrams and figures on this assessment are not necessarily drawn to scale. DRAFT D. 36 ft

END PART II

2008–2009 27 Clark County School District Revised 07/22/2009 Geometry H 2008–2009 Semester 2 Assessment — Released Free Response DRAFT

1. Given trapezoid TRQP with parallel sides TR and PQ . Diagonals TQ and RP intersect at point Z. Draw the picture and explain why DZTR: D ZQP .

2008–2009 1 GO ON Clark County School District Revised 07/22/2009 Geometry H 2008–2009 Semester 2 Assessment — Released Free Response DRAFT

2. 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.

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

2008–2009 2 Clark County School District Revised 07/22/2009