Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Geometry - Semester 2 Final Review -

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. If parallelogram EFGH is a rhombus and not a square, which of the following is true?

a. EG ⊥FH d. m∠H = 90°

b. EG ≅ FH e. None correct

c. ∠E ≅ ∠F

____ 2. Choose the equation of a line that has slope of 1

2 and passes through (−3,2).

a. y = 1

2x +

7

2d. y = 2x +

1

2

b. y = 1

2x +

1

2e. None correct

c. y = 2x + 7

2

____ 3. Which point lies on the line defined by (x,y,z) = (5,−1,0) + t(−1,2,3)?

a. (6, 1, –3) d. (7, –5, –6)

b. (4, –3, 3) e. None correct

c. (9, –5, –5)

____ 4. Which of the following is the mapping notation for a transformation of a reflection T across the y-axis?

a. T: x,yÊËÁÁ ˆ

¯˜̃ → −x,yÊ

ËÁÁ ˆ

¯˜̃ c. T: x,yÊ

ËÁÁ ˆ

¯˜̃ → y,xÊ

ËÁÁ ˆ

¯˜̃

b. T: x,yÊËÁÁ ˆ

¯˜̃ → −x,−yÊ

ËÁÁ ˆ

¯˜̃ d. T: x,yÊ

ËÁÁ ˆ

¯˜̃ → x,−yÊ

ËÁÁ ˆ

¯˜̃

____ 5. If (9, 11) is a point on K and the center of K is K(9,6), then which of the following could be an

equation for K?

a. (x + 9)2+ (y + 11)

2= 25

b. (x − 9)2+ (y − 11)

2= 25

c. (x + 9)2+ (y + 6)

2= 25

d. (x − 9)2+ (y − 6)

2= 25

e. None correct

Name: ________________________ ID: A

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____ 6. Find the circumference and area of the circle to the nearest tenth. Use 3.14 for π .

a. C = 452.2 ft; A = 75.4 ft 2 c. C = 37.7 ft; A = 113.0 ft 2

b. C = 75.4 ft; A = 452.2 ft 2 d. C = 113.0 ft; A = 37.7 ft 2

____ 7. Estimate the area of the irregular figure. Each square represents 1 square unit.

a. about 22 square units c. about 28 square units

b. about 34 square units d. about 30 square units

____ 8. Tell whether the given side lengths form a right triangle.

7, 11, 14

a. No b. Yes

Name: ________________________ ID: A

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____ 9. Given ∆ABC ∼ ∆JKL, find the perimeter of ∆JKL.

a. P = 42 ft c. P = 18.7 ft

b. P = 40.5 ft d. P = 9 ft

____ 10. Find the probability of the spinner landing on “new house”. Give your answer as a fraction.

a.16 c.

1

3

b. 60 d.1

4

Name: ________________________ ID: A

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____ 11. Solve for x.

a. x = 87.5 c. x = 42.5b. x = 90 d. x = 27.5

____ 12. Given ∆ABC with AB = 3, BC = 5, and AC = 6, find the length of midsegment XY .

a. XY = 3 c. XY = 2.5

b. XY = 1.5 d. XY = 2

____ 13. The Fun Guys game rental store charges an annual fee of $25 plus $5.50 per game rented. The Game Bank

charges an annual fee of $49 plus $2.50 per game. For how many game rentals will the cost be the same at

both stores? What is that cost?

a. 6 games; $58 c. 7 games; $64

b. 3 games; $42 d. 8 games; $69

Name: ________________________ ID: A

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____ 14. Find the area of the trapezoid.

a. 60 m2 c. 9 m2

b. 180 m2 d. 45 m2

____ 15. Tell whether a triangle with side lengths 6, 8, and 7 is an acute, obtuse, or a right triangle.

a. acute triangle b. obtuse triangle c. right triangle

____ 16. A fish in a river swims at a rate of 6 miles per hour. The river current moves 4 miles per hour in the

opposite direction from the fish. How fast is the fish traveling over the ground below?

a. 6 miles per hour c. 10 miles per hour

b. 11 miles per hour d. 2 miles per hour

____ 17. Find the area of the rhombus.

a. (16x2+ 48x + 16) cm

2c. (96x

3) cm

2

b. (16x2+ 24x + 8) cm

2d. (32x

2+ 48x + 16) cm

2

Name: ________________________ ID: A

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____ 18. Find the surface area of the cylinder. Use 3.14 for π. Round your answer to the nearest tenth.

a. 659.4 m2 c. 813.3 m2

b. 549.5 m2 d. 1318.8 m2

____ 19. Graph the line that has a slope of 2

3 and passses through the point (–3, –5).

a. c.

b. d.

Name: ________________________ ID: A

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____ 20. Find the geometric probability of the spinner landing on a two.

a. 10% d. None correct

b. 30% e. 20%

c. 40%

____ 21. Find the number of faces, edges, and vertices for the polyhedron.

a. vertices: 6

edges: 18

faces: 12

c. vertices: 12

edges: 18

faces: 8

b. vertices: 6edges: 12

faces: 18

d. vertices: 18edges: 6

faces: 12

____ 22. Use Euler’s Formula to determine how many faces a polyhedron with 12 edges and 9 vertices has.

a. 21 faces d. 108 faces

b. None correct e. 23 faces

c. 5 faces

Name: ________________________ ID: A

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____ 23. An artist designs a rectangular quilt piece with different types of ribbon that go from the corner to the center

of the quilt. The dimensions of the rectangle are AB = 10 inches and AC = 14 inches. Find BX .

a. BX = 7 inches c. BX = 5 inches

b. BX = 10 inches d. BX = 14 inches

____ 24. Find the area of the parallelogram.

a. 41 m2 c. 182 m2

b. 91 m2 d. 20.5 m2

____ 25. Find the least common multiple (LCM) of 4 and 6.

a. 24 c. 48

b. 2 d. 12

Name: ________________________ ID: A

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____ 26. Find the distance from P(–2, 1) to the line x = 3.

a. 4 c. 5

b. 9 d. 2

____ 27. Identify the pairs of congruent angles and proportional corresponding side lengths.

a. ∠B ≅ ∠D, ∠C ≅ ∠E, ∠A ≅ ∠F, EF

AC=DF

AB=DE

BC=3

4

b. ∠B ≅ ∠D, ∠C ≅ ∠E, ∠A ≅ ∠F, AC

EF=AB

DF=BC

DE=3

4

c. ∠B ≅ ∠D, ∠C ≅ ∠E, ∠A ≅ ∠F, EF

AB=DF

AC=DE

BC=1

2

d. ∠B ≅ ∠D, ∠C ≅ ∠E, ∠A ≅ ∠F, AC

EF=DF

AB=DE

BC=4

3

Name: ________________________ ID: A

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____ 28. Graph and find the area of the figure with the vertices (–2, –3), (–1, 2), (1, 2), (2, –3).

a.

A = 15 units2

c.

A = 11 units2

b.

A = 20 units2

d.

A = 30 units2

Name: ________________________ ID: A

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____ 29. Find the area of the circle to the nearest tenth. Use 3.14 for π.

a. 695.7 cm2 c. 52.8 cm2

b. 886.2 cm2 d. 221.6 cm2

____ 30. What is the included angle of AD and CD?

a. ∠C c. ∠A

b. ∠D d. ∠B

____ 31. Solve for q in the equilateral triangle.

a. q = 100° c. q = 20°

b. q = 60° d. q = 10°

Name: ________________________ ID: A

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____ 32. Compare the volumes of the cylinders.

a. Cylinder N has a greater volume than Cylinder M.

b. Cylinder M has a greater volume than Cylinder N.

c. The volumes are equal.

____ 33. ABCD and EFGH are similar polygons. Their corresponding sides have a ratio of 2:3. If the perimeter of

ABCD is 54 inches, what is the perimeter of EFGH?

a. 108 inches c. 81 inches

b. 36 inches d. 162 inches

____ 34. The Yield sign has a shape of an equilateral triangle with side length of 36 inches. What is the height of the

sign? Will a rectangular metal sheet of 36 × 32 inches be big enough to make one sign?

a. The Yield sign is about 33.7 inches tall. So the rectangular metal sheet will not be big

enough to make one sign.

b. The Yield sign is about 31.2 inches tall. So the rectangular metal sheet will be big

enough to make one sign.

c. The Yield sign is about 25.5 inches tall. So the rectangular metal sheet will be big

enough to make one sign.

d. The Yield sign is about 50.9 inches tall. So the rectangular metal sheet will not be big

enough to make one sign.

Name: ________________________ ID: A

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____ 35. Find the number of faces, edges, and vertices for the polyhedron.

a. 4 faces, 4 edges, and 6 vertices c. 6 faces, 4 edges, and 4 vertices

b. 4 faces, 4 edges, and 4 vertices d. 4 faces, 6 edges, and 4 vertices

____ 36. Janice is going on vacation and needs to leave her dog at a kennel. Nguyen’s Kennel charges $15 per day

plus $20 for a processing fee. The Pup Palace Kennel charges $12 per day, and has a $35 processing fee.

After how many days is the Pup Palace Kennel cheaper than Nguyen’s Kennel?

a. The Pup Palace Kennel is always cheaper than Nguyen’s Kennel.

b. The Pup Palace Kennel is never cheaper than Nguyen’s Kennel.

c. The Pup Palace Kennel is cheaper than Nguyen’s Kennel after 15 days.

d. The Pup Palace Kennel is cheaper than Nguyen’s Kennel after 5 days.

____ 37. Find x.

a. 70° c. 116°

b. 58° d. 110°

Name: ________________________ ID: A

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____ 38. Identify the diameters in circle R.

a. VN c. TV , NH

b. HV , TN , NV d. RV , RH , RT , RN

____ 39. Which of the following is the most descriptive name for figure MNOP with vertices M(−3,5), N(0,9), O(4,6),

and P(1,2)?

a. parallelogram c. rhombus

b. rectangle d. square

____ 40. Find the circumference of the circle to the nearest tenth. Use 3.14 for π.

a. 631 in. c. 25.1 in.

b. 50.2 in. d. 201 in.

____ 41. Lucia visits the park every 8 days and goes to the library every 7 days. If Lucia does both of these today, how

many days will pass before Lucia gets to do them both on the same day again?

a. 56 days c. 15 days

b. 112 days d. 1 day

Name: ________________________ ID: A

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____ 42. Find the surface area of the prism.

a. 3240 cm2 c. 504 cm2

b. 7776 cm2 d. 3024 cm2

____ 43. Multiply.

(d + 3)(d – 3)

a. d2 – 9 c. 2d2 – 9d

b. d2 – 6d – 9 d. d2 + 6d + 9

____ 44. A point is chosen randomly on AC. Find the probability that the point is not on AB.

a.1

4c. 6

b. 3 d.3

4

____ 45. Translate the triangle with vertices A(3, 4),B(2, − 1), andC(4, 12) along the vector −1, 3 . Find the

coordinates of the new image.

a. A′(2, 7),B′(1, 2), andC ′(3, 15) c. A′(4, 7),B′(3, − 2), andC ′(5, 15)

b. A′(−3, 12),B′(−2, − 3), andC ′(−4, 36) d. A′(6, 3),B′(5, − 2), andC ′(7, 11)

____ 46. A tree casts a shadow of 26 meters when the angle of elevation of the sun is 20°. Find the height of the tree to

the nearest meter.

a. 24 m c. 9 m

b. 231 m d. 11 m

Name: ________________________ ID: A

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____ 47. An eagle 300 feet in the air spots its prey on the ground. The angle of depression to its prey is 15 °. What is

the horizontal distance between the eagle and its prey? Round to the nearest foot.

a. 1,120 ft c. 310 ft

b. 1,159 ft d. 723 ft

____ 48. Find the coordinates of the image of the point (3,7) when it is reflected across the line y = 12.

a. (3, 17) c. (3, − 7)

b. (3, 19) d. (3, − 5)

____ 49. Write the equation of a circle with center M(4, – 2) and radius 5.

a. (x + 4)2+ (y − 2)

2= 25 c. (x − 4)

2+ (y + 2)

2= 5

b. (x − 4)2+ (y + 2)

2= 25 d. (x + 2)

2+ (y − 4)

2= 25

____ 50. Find m∠A.

a. m∠A = 40° c. m∠A = 75°b. m∠A = 80° d. m∠A = 20°

Name: ________________________ ID: A

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____ 51. Find CA.

a. CA = 10

b. CA = 12

c. CA = 14

d. Not enough information. An equiangular triangle is not necessarily equilateral.

____ 52. Solve for x in the isosceles triangle.

a. x = 11.7° c. x = 68°

b. x = 118° d. x = 18°

____ 53. Add the vectors a→

= −4,3 , b→

= 2,−9 , and c→

= 7,5 .

a. −13,−1 c. 5,−1

b. 5,7 d. −13,7

Name: ________________________ ID: A

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____ 54. A photograph measure 4 inches by 5 inches. If it is enlarged by 200%, what are its new measurements?

a. 2 by 2.5 c. 9 by 11.25

b. 8 by 10 d. 6 by 7

____ 55. Find θ to the nearest degree.

a. 35° c. 42°b. 25° d. 65°

____ 56. A 35-foot telephone pole casts a 46-foot shadow on the ground while the sun is shining. To the nearest

degree, what is the angle of elevation θ of the sun from the end of the shadow?

a. 37° c. 40°b. 50° d. 53°

____ 57. Find sinθ if cosθ = 0.6. Round your answer to the nearest hundredth.a. sinθ ≈ 0.40 c. sinθ ≈ 0.64b. sinθ ≈ 0.80 d. sinθ ≈ 0.63

____ 58. Find the surface area of a sphere with volume 166.67π m3. Give your answer in terms of π .

a. 500 m2 c. 100 m2

b. 5π m2 d. 100π m2

Name: ________________________ ID: A

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____ 59. A point B(3,8) is translated 4 units to the right. What are the coordinates of the new image?

a. B' (−1,8) c. B' (3,4)

b. B' (3,12) d. B' (7,8)

____ 60. What is the volume of a hemisphere with an 2-centimeter diameter? Round to the nearest

hundredth of a cubic centimeter.

a. 4.19cm3

d. 16.76cm3

b. 2.09cm3

e. None correct

c. 33.51cm3

ID: A

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Geometry - Semester 2 Final Review -

Answer Section

MULTIPLE CHOICE

1. A

2. A

3. D

4. A

5. D

6. C

7. A

8. A

9. A

10. A

11. C

12. B

13. D

14. D

15. A

16. D

17. B

18. C

19. B

20. E

21. C

22. C

23. A

24. B

25. D

26. C

27. A

28. A

29. D

30. B

31. C

32. A

33. C

34. B

35. D

36. D

37. B

38. C

39. D

ID: A

2

40. B

41. A

42. D

43. A

44. A

45. A

46. C

47. A

48. A

49. B

50. A

51. C

52. C

53. C

54. B

55. B

56. A

57. B

58. D

59. D

60. B