GeometrySemester2FinalAssignmentIt is very important that you review for the Geometry Final. Here are a few pieces of information you want to know.

� Your Final is worth 15% of your overall grade � The final covers concepts from the entire semester, they are the following

o Unit 7 – Similarity o Unit 8 – Right Triangles o Unit 9 – Areas and Surface Areas o Unit 10 – Volumes o Unit 11 – Circles o Unit 12 – Probability

� The final is 45 multiple choice problems, here are some tips for multiple choice problems o Read the question before you look at the answer o Come up with the answer in your head before looking at the possible answers, this way the

choices given on the test won't throw you off or trick you o Eliminate answers you know aren't right o Read all the choices before choosing your answer o If there is no guessing penalty, always take an educated guess and select an answer

Finals Schedule Tuesday, June 9th, 2014 1st period EXAM 7:45 - 9:30 2nd period 9:40 -10:19 3rd period 10:24 -11:03 4th period 11:08 -11:47 Lunch 11:47 -12:27 5th period 12:27-1:06 6th period 1:11 -1:50 7th period 1:55 -2:35

Wednesday, June 10th, 2014 2nd period exam 7:45 - 9:30 Break 3rd period exam 9:40 -11:25 Thursday, June 11th, 2014 4th period exam 7:45 - 9:30 Break 5th period exam 9:40- 11:25 Friday, June 12th , 2014 6th period exam 7:45 - 9:30 Break 7th period exam 9:40 -11:25

This Assignment is due on the day of your final and is worth 500 assignment points. Make sure you show your work for full credit, circling the correct answer is not enough. Assigned problems for each day of the Finals Review Date Problems to do that evening Monday, June 1 1, 3, 4, 5, 6, 7, 8, 9, 10, 18 Tuesday, June 2 11, 12, 13, 14, 15, 16, 17 Wednesday, June 3 19, 20, 21, 22 Thursday, June 4 2, 23, 24, 25, 26, 27, 28, 29, 30 Friday, June 5 31, 32, 33, 34, 35, 36, 37, 38, 47 Monday, June 6 39, 40, 41, 42, 43, 44, 45, 46

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Multiple Choice: Identify the choice that best completes the statement or answers the

question. Figures are not necessarily drawn to scale.

1. The ratios of the areas of triangle A to triangle B is ����. If the area of triangle B is 100��,

what is the length of a side of triangle A?

A. 4� C. 10�

B. 8� D. 64�

2. What is the ratio of the volumes of the two cubes? The cubes have edges of lengths 3 inches and 7 inches.

A. 3: 7

B. 6: 14

C. 9: 49

D. 27: 343

3. What is the scale factor of the dilation of ∆��� to image ∆�′�′�′ ?

A. −2

B. 1

C. 2

D. 3

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4. Apply the dilation �:��, �� → �4�, 4�� to the polygon with the given vertices. Name the coordinates of the image points.

A. ���8, 4�, ���16, 4�, ���16, −12�

B. ���8, 4�, ���16, 4�, ���16, 12�

C. ���0.5, 0.25�, ���1, 0.25�, ���1, −0.75�

D. ���0.5, 0.25�, ���1, 0.25�, ���1, 0.75�

5. The pair of triangles is similar. What is the value for � ?

A. � = 18

B. � = 16

C. � = 13

D. � = 3

6. In the figure, ∆��#~∆���. What is the length of side ��%%%% ?

A. �� = 6

B. �� = 7

C. �� = 16

D. �� = 20

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7. Two triangles are similar and the ratio of each pair of corresponding sides is 2: 1 . Which statement regarding the two triangles is not true?

A. Their areas have a ratio of 4: 1

B. The scale factor is a ratio of 2: 1

C. Their perimeters have a ratio of 2: 1

D. Their corresponding angles have a ratio of 2: 1

8. What is the value of & ?

A. & = 39

B. & = 54

C. & = 63

D. & = 90

9. In ∆'(), * is the midpoint of '(%%%%, + is the midpoint of ()%%%%%, and R is the midpoint of ')%%%%. Given the following, what is the perimeter of ∆,*+ ?

• '* = 8.2� • *+ = 4.3� • () = 6�

A. 11.4�

B. 15.5�

C. 18.4�

D. 18.5�

10. In the figure, ∆��� is a right triangle and ∆���~∆��� . What is the length of ��%%%% ?

A. �� = 20

B. �� = 40

C. �� = 10√20

D. �� = 2√10

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11. In the right triangle, � and � represent unknown side lengths. What is the length of side � ?

A. 2

B. 4

C. 2√3

D. 3√2

12. In the figure, what is the distance a ball travels when thrown from second base to home plate?

A. 90.//0

B. 180.//0

C. 90√2.//0

D. 2√90.//0

13. What is cos �° in the triangle?

A.

4041 C.

419

B. 9

41 D. 9

40

14. Which of the following has the same value as sin ( ?

A. sin )

B. tan (

C. cos )

D. cos (

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15. What is the measure of angle A in the triangle, rounded to the nearest degree?

A. 35°

B. 44° C. 46° D. 72°

16. A person is standing at ground level with the base of the Empire State Building in New York City. The angle formed by the ground and a line segment from his position to the top of the building is 48.4°. The height of the Empire State Building is 1472 feet. Find the distance that he is standing from the base of the Empire State Building to the nearest foot.

A. 8.//0 C. 1968.//0

B. 1307.//0 D. 2217.//0

17. Find the value of x in the diagram below. Round your answers to the nearest tenth if necessary.

A. � = 12.2

B. � = 13.1

C. � = 24.5

D. � = 26.2

18. In a large city, a circle with a radius of 39:/; contains a population of 30,348 people. What is the expected population of a circle with a 49:/ radius in the same city?

A. 121,392</=<:/ C. 53,952</=<:/

B. 91,044</=<:/ D. 40,464</=<:/

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19. What is the area of a regular hexagon with an apothem of 10�

and a side length of �>√?

? � ?

A. 200√3��

B. 300√3��

C. 600√3��

D. 600��

20. Given that the side of the regular pentagon is 8.0 and that the apothem is approximately 5.51.0, what is the approximate area of the shaded triangle?

A. 20.0�

B. 22.0�

C. 64.0�

D. 110.0�

21. What best describes the cross section shown on the cube?

A. square C. trapezoid

B. triangle D. rectangle

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22. A layered cake is a solid of revolution. Which of the following is the drawing of a two-dimensional shape and an axis of rotation that could form the cake?

A.

C.

B.

D.

23 Jamal wants to fill a container with two different colors of sand for an art project. The container is 99&�@/; tall and has a regular polygon base. He is going to fill part of the container with 109&? of blue sand. How much green sand does Jamal need to purchase to fill the rest of the container? Round your answer to the nearest tenth if necessary.

A. 36.89&?

B. 449&?

C. 46.89&?

D. 549&?

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24. Compare the volumes of the cone and the regular pyramid below. Which statement is true?

@/9A@0129&�@/; BCD9E;79&�@/;

@/9A@079&�@/; ;9D/:/&A0@129&�@/;

A. The volume of the pyramid is about 1409&? more than the volume of the cone.

B. The volume of the cone is about 279.89&? more than the volume of the pyramid.

C. The volume of the cone is about 531.89&? more than the volume of the pyramid.

D. The volume of the cone is about 1129&? more than the volume of the pyramid.

25. A tanker truck can carry 3,000AC::=&; of fuel and is going to fill an empty cylindrical gas tank with a height of 4.//0. The operator doesn’t know the radius of the tank and is unsure whether the tank will be able to hold all of the fuel. When the height of the fuel in the tank reaches 1.==0, the operator looks at the pumping gauge and determines that approximately 846AC::=&; of fuel were pumped into the tank. Based on this information will all 3,000AC::=&; of fuel fit in the tank? Explain.

A. Yes, the tank can hold a total of 4,280AC::=&; of fuel.

B. Yes, the tank can hold a total of 3,384AC::=&; of fuel.

C. No, the tank can only hold a total of 2,538AC::=&; of fuel.

D. No, the tank can only hold a total of 2,154AC::=&; of fuel.

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26. Three students were asked to find the volume of a cylinder with a hemisphere removed from one end.

Each student’s work is shown below. Determine which student is correct.

Student X Student Y Student Z

F=:E/ = GB�@ − 12 H4

3 GB?I

= G ∙ 5� ∙ 6 − 12 H4

3 G ∙ 5?I

= 150G − 12 H500

3 GI = 150G − 250

3 G = 200

3 G9&?

F=:E/ = GB�@ − 43 GB?

= G ∙ 3� ∙ 10 − 43 G ∙ 3?

= 90G − 36G = 54G9&?

F=:E/ = GB�@ − 12 H4

3 GB?I

= G ∙ 3� ∙ 10 − 12 H4

3 G ∙ 3?I

= 90G − 12 �36G�

= 90G − 18G = 72G9&?

A. Student X is correct.

B. Student Y is correct.

C. Student Z is correct.

D. None of the students is correct.

27. What is the height of a square pyramid that has a side length of 13.//0 and a volume of 1521.0? ?

A. @ = 3.//0 C. @ = 27.//0

B. @ = 9.//0 D. @ = 39.//0

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28. A food manufacturer sells yogurt in cone shaped cups with the dimensions shown. To the nearest tenth, how many fluid ounces of yogurt does the cup hold if 1�? ≈ 0.034.:=L ?

A. 0.6.:=L

B. 5.7.:=L

C. 17.1.:=L

D. 22.8.:=L

29. What is the volume of the sphere in terms of � ?

A. 36G�?.0?

B. 48G�?.0?

C. 288G�?.0?

D. 864G�?.0?

30. You want to design a cylindrical container for oatmeal that has a volume of 909&?. You also want the height of the container to be 3.5 times the radius. To the nearest tenth, what should the approximate radius of the container be?

A. 2.09& C. 3.09&

B. 2.99& D. 3.19&

31. Given mAC = mBC and ∠��� is a central angle, what is the value of � and BC ?

A. � = 18, mBC = 136°

B. � = 9.2, mBC = 88° C. � = 18, mBC = 88° D. � = 9.2, mBC = 136°

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32. In the figure below, ∠NO, is a circumscribed angle. Find the value of x.

A. � = 3.5

B. � = 5C. � = 8.5

D. � = 12

33. What is the measure of RS ? A. 54°

B. 38° C. 32° D. 27°

34. What is the measure of the inscribed angle ���, if the ray is tangent to the circle?

A. 140°

B. 110° C. 70° D. 55°

35. What is the length of the minor arc AB in the circle with a radius of 45� ?

A. 20G�

B. 10G�

C. 5G�

D. 2G�

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36. What is the area of a circular pool that has a circumference of 100G.//0 ?

A. 10G.0� C. 100G.0�

B. 50G.0� D. 2500G.0�

37. The diameter of a circular pizza pan is 189&�@/;. Two-thirds of the pizza is eaten by your friends. What is the approximate area of the pizza pan that is covered by the remaining pizza?

A. 1709&� C. 549&�

B. 859&� D. 279&�

38. A circle has an arc length of 10.//0. The central angle formed is 60°. What is the area of the sector? (Hint: find the radius first)

A.

150G .0� C.

G360.0�

B. G

150.0� D. 900

G .0�

39. Given the square inside the circle with radius 6. What is the probability that the point lies inside the square, if a point is chosen at random inside the circle?

A.

72 − 36GG C. √2

G

B. 2 − G

G D. 2G

40. A grab bag contains 7 football cards and 3 basketball cards. An experiment consists of taking one card out of the bag, then selecting another card. What is the probability of selecting a football card, replacing it, and then selecting a basketball card? If necessary, round answers to the nearest hundredth.

A. 0.23 C. 0.21

B. 0.09 D. 0.49

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41. A bag contains hair ribbons for a spirit rally. The bag contains 5 black ribbons and 7 green ribbons. Lila selects a ribbon at random, then Jessica selects a ribbon at random from the remaining ribbons. Find the probability that both events � and � occur. Which is the correct answer in simplest fraction form?

#P/&0�:'9:C;/:/�0;CQ:C�RB9QQ=&. #P/&0�:S/;;9�C;/:/�0;CAB//&B9QQ=&.

A.

733 C.

35132

B. 35

144 D. 5

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42. The table shows the distribution of male and female students and left- and right-handed students in the math club. Find the probability that a female student selected at random is left-handed. Which is the correct answer as a fraction in simplest form?

Left-handed Right-handed Male 2 35

Female 6 36

A.

34 C.

16

B. 17 D.

679

43. The table shows the distribution of the labor force in the United States in the year 2000. Suppose that a worker is selected at random. Find the probability of randomly selecting a worker in the Industry field given that the worker is female. Which is the correct answer as a decimal rounded to the nearest thousandth?

Agriculture Industry Services Male 3,132,000 25,056,000 50,112,000

Female 667,000 8,004,000 57,362,000

A. 0.141 C. 0.121

B. 0.242 D. 0.312

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44. Events � and � are independent. Find the missing probability. O��� =_______ O��� = 0.3 O��C&D�� = 0.06

A. 0.7 C. 0.2

B. 0.24 D. 0.3

45. If O��� = 0.43 and O��|�� = 0.89, find O��C&D��.

A. 0.51 C. 0.11

B. 0.48 D. 0.38

46. The sections on a spinner are numbered from 1 through 8. If the probability of landing on a given section is the same for all the sections, what is the probability of spinning a number less than 4 or greater than 7 in a single spin?

A.

12 C.

38

B. 18 D.

58

47. Find the angle measures of ����.

A. ∠� = 71° ∠� = 54° ∠� = 109° ∠� = 126°

C. ∠� = 35° ∠� = 134° ∠� = 145° ∠� = 54°

B. ∠� = 34° ∠� = 54° ∠� = 146° ∠� = 126°

D. ∠� = 71° ∠� = 50° ∠� = 109° ∠� = 130°