Geometry Honors 2010 2011 Semester 2 Exam Released

Geometry Honors 2010–2011 Semester 2 Exam — Released Note: Diagrams on this exam are not necessarily drawn to scale.

BEGIN PART I (50 questions) 4. Determine the area of the right triangular garden. 1. A circle has a circumference of 36π centimeters. What is the radius of the circle? 13 m 5 m (A) 6 cm (B) 12 cm (A) 18 m2 (C) 18 cm (B) 30 m2 (D) 36 cm (C) 60 m2 2. In the figure below, the adjacent sides of (D) 65 m2 the polygon are perpendicular. 5. A framed picture is shown below.

2 in. 16 cm

12 in. 3 in. 3 in.

2 in. 28 cm 16 in. What is the perimeter of the polygon? What is the area of the picture (without the (A) 93 cm frame)? (B) 109 cm (A) 60 in2 (C) 116 cm (B) 80 in2 (D) 121 cm (C) 96 in2 3. (D) 192 in2

2010–2011 1 GO ON Clark County School District Revised 08/02/2011 Geometry Honors 2010–2011 Semester 2 Exam — Released Note: Diagrams on this exam are not necessarily drawn to scale.

6. What is the best description of DC in 9. The surface area of a square pyramid is 1 relation to the pyramid? given by the formula SA= B + Pℓ. 2 V

12 cm 13 cm

5 cm A D H F

B C What is the surface area of the pyramid?

(A) base edge (A) 285 cm2 (B) slant height (B) 300 cm2 (C) lateral edge (C) 340 cm2 (D) altitude (D) 360 cm2

7. The volume of a cylinder is given by the 10. The surface area of a cone is given by the 2 formula V= p r h . formula SA=p r2 + p rℓ.

3 cm 5 cm

What is the volume of the cylinder? 3 cm (A) 36π cm3 What is the surface area of the cone? (B) 48π cm3 (C) 72π cm3 (A) 24π cm2 (D) 192π cm3 (B) 21π cm2 (C) 18π cm2 8. (D) 9π cm2

11. A small spherical ball has a diameter of 14. Two similar pentagons have a scale factor 6 centimeters. What is the surface area of of 3:4. The larger pentagon has an area of the ball? 32 square feet.

SA= 4p r 2

(A) 144π cm2 (B) 48π cm2 (C) 36π cm2 (D) 24π cm2 What is the area of the smaller pentagon? 12. Water is poured into a cylindrical container until it is half full. (A) 8 ft2 (B) 12 ft2 V= p r2 h (C) 18 ft2 4 cm (D) 24 ft2

10 cm 15. 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 volume of the water?

(A) 14π cm3 10 in. 16 in. (B) 20π cm3 (C) 80π cm3 (D) 160π cm3

13. 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

16. Which accurately describes a radius? 19. Use circle O.

(A) A line that intersects a circle at two P points. Q (B) A line that intersects a circle at 82° exactly one point. O (C) A segment whose endpoints are points on the circle. T (D) A segment having an endpoint on the circle and an endpoint at the center of R the circle. Given m� RQP 82 , what is m RTP ? 17. Use circle C. (A) 41° (B) 82° (C) 98° E C (D) 164° B G 20. Use circle J.

A D (5x + 15)

Which is a diameter? 120 J s (A) AD s (B) AG K

(C) BC What is the value of x? (D) BE (A) 9 18. (B) 21 (C) 27 (D) 45

(D) 97° 21. In circle N, mJM=(6 x + 5) , 23. mKL=(10 x + 3) , and m� KHL 140 .

What is the value of x?

(A) 8.25 (B) 9.25 (C) 17 (D) 18

22. In the figure below, mJK = 66 and mMN =128 .

M J H L

What is m H ?

(A) 31° (B) 62° (C) 64°

24. Two tangents are drawn from point D to circle A.

What conclusion is guaranteed by this diagram?

(A) AD = BD (B) AC = DC 1 (C) mBC= m BDC 2 (D) D ABD is a right triangle.

27. 25. Points B, D, F, and H are points of tangency to circle J. AB = 17, CE = 42, EG = 23, and GA = 29.

x C 17

J 42 29 H D F E G 23

(A) 14 (B) 17 (C) 25 (D) 31

26. In circle C, UW = XZ, VW = 2x + 14, and XY = 6x + 2.

W V X U

(A) 5 (B) 4 (C) 3 (D) 2

(D) reflection 28. WY is a diameter of circle C. m� ZCY+ (2 x 10) , m� WCZ- (4 x 10) , and m� YCX- (2 x 4) .

(A) 22 (B) 30 (C) 32.5 (D) 43.5

29. Determine the single transformation that has mapped D ABC to D Aⅱ B C .

A′ B

C C′ B′

(A) translation (B) rotation (C) dilation

(D) 30. How many lines of symmetry does a square have?

(A) 0 (B) 1 (C) 2 (D) 4 32. 31. Which pair of figures is similar but NOT congruent?

(A) 8 3

(B) 30° 8 3

33. The figures below are similar.

C 3 D 3 3 B V E 4 4 6 6 Z W 2 2 A Y 2 X

What is the scale factor of ABCDE to VWXYZ?

(A) 3:2 (B) 3:6 (C) 4:2 (D) 4:3

34. 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.

P = 400 cm

What is the length x?

(A) 45 cm (B) 80 cm (C) 90 cm (D) 100 cm

35. The measures of the angles of a triangle have the ratio 1:3:5. What is the measure of the largest angle?

(A) 50° 3 m 12 m How tall is the tree?

(A) 8 m (B) 10 m (B) 60° (C) 11 m (D) 14 m

38. (C) 90°

(D) 100°

36. 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

37. 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.

39. 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.

8 ft 32 ft

What is the height of the tree?

(A) 20 ft (B) 29 ft (C) 45 ft (D) 51 ft

40. Use the figures below.

V W R T

What measure for W would make DRST ~ D WUV ?

(A) 34° (B) 56° (C) 68° (D) 112°

41. In triangle QRS, RT bisects QRS . 44. What is the geometric mean of 4 and 16?

R (A) 8 (B) 10 w 4 (C) 8 (D) 20 Q 3 T 6 S 45. Fred stands at corner A of a rectangular What is the value of w? field. He wants to walk to the opposite corner C. (A) 7 (B) 8 A B (C) 9 5 yd (D) 12

D 12 yd C 42. In triangle PQR, JGP QR . What is the shortest distance from A to C? Q (A) 7 yd J (B) 12 yd 9 (C) 13 yd x (D) 17 yd

R 6 G 12 P

(A) 3 (B) 6 (C) 15 (D) 18

48. 46. A rectangular prism has dimensions as shown.

9 cm A 12 cm

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

(A) 14 cm (B) 25 cm (C) 32 cm (D) 41 cm

47. Use the dimensions given in the diagram below.

(A) 3 (B) 5 (C) 12 (D) 17

49. The three sides of a triangle are 11 inches, 11 inches, and 11 inches. Which is a classification for this triangle? (A) acute (B) obtuse (C) right (D) scalene

50. Use the triangle below.

d 12 3

60°60°

What is the value of d ?

(A) 12 (B) 24 (C) 24 2 (D) 24 3

51. Use the dimensions given in the diagram. 54. Use the table and the dimensions given in the diagram.

1000 y 4 2 r

10° 45° 30º q sin  cos  tan  What is the value of y? 10° .1736 .9848 .1763 20° .3420 .9397 .3640 (A) 4 30° .5000 .8660 .5774 40° .6428 .7600 .8391 (B) 4 2 (C) 4 3 What is the approximate value of r? (D) 8 (A) 174 (B) 342 52. The square below has diagonal length of (C) 500 5 2 meters. (D) 985

What is the length of a side?

(A) 5 m (B) 10 m (C) 5 2 m (D) 5 3 m

55. Use the dimensions given in the right 57. Use the table and the dimensions given in triangle below. the diagram below.

B 13 5 100 ft 64 ft A 12 C

What is the tangent of B ? 

5 (A) 13 q sin  cos  tan  5 10° .1736 .9848 .1763 (B) 20° .3420 .9397 .3640 12 30° .5000 .8660 .5774 13 40° .6428 .7600 .8391 (C) 5 What is the kite’s approximate angle of 12 elevation? (D) 5 (A) 10° 56. (B) 20° (C) 30° (D) 40°

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

x h 50° A C 75 30º Which equation would be used to find the 100 yd length of x? q sin  cos  tan  (A) x = 75tan 50 10° .1736 .9848 .1763 20° .3420 .9397 .3640 (B) x = 75sin 50 30° .5000 .8660 .5774 40° .6428 .7600 .8391 75 (C) x = tan 50 What is the approximate height h of the 75 structure? (D) x = sin 50 (A) 50 yd (B) 58 yd 59. (C) 83 yd (D) 87 yd

61. In circle D, AB is tangent at A, and CB is tangent at C.

A 15 B

What is the length of BD ?

(A) 23 (B) 17 (C) 16 (D) 15

62. 63. In circle D, AB is tangent at A, and BC is tangent at C.

3x + 6 12

6x – 12 C

(A) 2 (B) 4 (C) 6 (D) 12

64. In the figure below, AC and EC are secants of the circle.

20 m 4 m A B C 3 m D x E

What is DE?

(A) 15 m (B) 18 m (C) 29 m (D) 32 m

END PART I

GO ON TO PART II

BEGIN PART II (10 questions) 3. All triangles below are regular. What is the probability that a randomly thrown dart 1. The target below is a regular quadrilateral. hitting the figure will land in the shaded region? 5 cm 5 cm

7 (A) What is the probability that a randomly 16 thrown dart hitting the target will land in 9 the shaded region? (B) 16 1 9 (A) (C) 4 13 1 3 (B) (D) 3 4 2 (C) 5 4. In the square below, all adjacent circles are congruent, externally tangent to each other, 1 (D) and outer circles are tangent to the square. 2 The area of the shaded region is 576- 144p square centimeters. 2.

What is the radius of each circle?

(A) 4 cm (B) 8 cm (C) 12 cm (D) 16 cm

7. 5. A water tower consists of a cylinder and a cone. The radius of each is the same.

What is the volume of the water tower?

(A) 26π m3 (B) 29π m3 (C) 33π m3 (D) 36π m3

6. A cinder block is in the shape of a rectangular prism. It has two identical holes passing through it, also in the shape of rectangular prisms.

6 in. 4 in.

8 in. 16 in.

What is the volume of the cinder block in cubic inches?

(A) 192 in.3 (B) 384 in.3 (C) 640 in.3 (D) 1024 in.3

8. Use the dimensions given in the diagram of a right trapezoid.

135° 7 cm

What is the area of the trapezoid?

(A) 36 cm2 (B) 36 2 cm2 (C) 72 cm2 (D) 72 2 cm2

9. Given a 45º-45º-90º triangle, what is the tangent of the 45º angle?

1 (A) 2 (B) 1 2 (C) 2 (D) 2

10. A circle is centered at (9,- 7) . The point (5,- 7) is on the circle. What is the equation of the circle?

2 2 (A) ( x-5) +( y + 7) = 4

2 2 (B) ( x-5) +( y + 7) = 16

2 2 (C) ( x-9) +( y + 7) = 4

2 2 (D) ( x-9) +( y + 7) = 16

11. The patio shown below needs a wood border.

2 ft 2 ft 1 ft 2 ft

How many feet of wood are needed to make the border?

(A) 26 ft (B) 28 ft (C) 26 + 2 2 ft (D) 28 + 2 2 ft

12. One person is 100 feet away from a building looking at the q sin  cos  tan  10° .1736 .9848 .1763 top of the building at a 40° angle. Another person is 400 20° .3420 .9397 .3640 feet 30° .5000 .8660 .5774 40° .6428 .7600 .8391

away looking at the top of the building’s antenna tower at a 20° angle.

40° 20° 100 ft 400 ft

What is the approximate height h of the antenna tower?

(A) 62 ft (B) 73 ft (C) 146 ft (D) 299 ft

END PART II

2010–2011 24 GO ON Clark County School District Revised 08/02/2011 Geometry Honors 2010–2011 Semester 2 Exam — Released Free Response

1. This question obsolete as of 2011–2012. See new test specifications and practice questions.

2010–2011 1 GO ON Clark County School District Revised 08/02/2011