1. If a Triangle Is Formed with the Given Side Lengths, Which Would Be a Right Triangle?

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Geometry Final 2010

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1. If a triangle is formed with the given side lengths, which would be a right triangle?

A. 4 in., 7.5 in. and 8.5 in.

B. 2.8 in., 3.6 in. and 4.5 in.

C. 4.5 in., 6 in. and 8.5 in.

D. 2.5 in., 6 in. and 7.5 in.

2. The three squares below when joined at their vertices form a right triangle.

What is the area of the shaded square?

A. 402 cm2

B. 372 cm2

C. 100 cm2

D. 10 cm2

3. Find the value of x. Round your answer to the nearest tenth of a cm.

A. 15 cm.

B. 21.2 cm.

C. 22.5 cm.

D. 450 cm.

4. The drawing below shows James’ mailbox and the brace he used to secure it to the post.

Which is closest to the value of x, this distance from the bottom of the brace to the mailbox?

A. 11 in.

B. 17 in.

C. 19 in.

D. 25 in.

5. Classify this triangle by its angle measures and side lengths.

A. Acute equilateral

B. Acute isosceles

C. Right scalene

D. Right isosceles

6. Which statement is true about the triangle below?

A. is 45o

B. is 90o

C. is 30o

D. is 60o

7. Find the measure of in the figure below.

A. is 68o

B. is 22o

C. is 90o

D. is 158o

8. Find the side lengths of the triangle below.

A. -11 in., 1 in., 2 in.

B. 9 in., 3 in., 3 in.

C. 19 in., 19 in. 13 in.

D. 5 in., 5 in., 2 in.

9. Classify this triangle by its angle measures and side lengths.

A. Acute scalene

B. Obtuse scalene

C. Acute isosceles

D. Obtuse isosceles

10. Find and.

11. Arrange the angle measures of the triangle below from smallest to largest.

12. What is the measure of and what is the reason for your conclusion?

A. , supplementary angles.

B. , complementary angles.

C. , supplementary angles.

D. , complementary angles.

13. Which of the following lengths would form a triangle with the two given sides?

A. 5 in.

B. 6 in.

C. 7 in.

D. 8 in.

14. Use the diagram of the staircase railing below to answer the following:

Which is a true statement about the measure of ?

A. It equals 150º by the Same Side Interior Angles Theorem

B. It equals 30º by the Alternate Interior Angles Theorem

C. It equals 30º by the Corresponding Angles Postulate

D. It equals 150º by the Supplementary Angles Theorem.

15. Find the value of x.

16. The area of the square is 100 square meters. What is its perimeter?

A. 10 meters

B. 20 meters

C. 40 meters

D. 60 meters

17. A spherical ball has a diameter of 10 centimeters. Which is closest to the volume of the ball?

A. 524 cm3

B. 393 cm3

C. 4189 cm3

D. 105 cm3

18. A triangular prism is shown below.

What is the volume in cubic inches?

A. 48 in3

B. 24 in3

C. 60 in3

D. 30

19. A company designed a new label to completely cover the lateral surface area of a cylindrical can without any overlap. The can is 5.5 inches tall and 3 inches in diameter. Which of the following is closes to the area of this new label?

A. 52 in2

B. 160 in2

C. 104 in2

D. 66 in2

20. Which statement best describes how the volume of a cube changes when the edge length is doubled to form a new cube?

A. The volume of the new cube is ½ the volume of the original cube.

B. The volume of the new cube is ¼ the volume of the original cube.

C. The volume of the new cube is 8 times the volume of the original cube.

D. The volume of the new cube is 4 times the volume of the new cube.

21. The figure shows a right circular cone on top of a hemisphere with the same radius.

To the nearest whole number, what is the total volume of this solid?

A. 201 cm3

B. 256 cm3

C. 278 cm3

D. 309 cm3

22. The radius of a spherical beach ball is 24 cm. If another spherical beach ball has a radius of 3 cm. longer, about how much greater is its surface area, to the nearest cm?

A. 37 cm2

B. 113 cm2

C. 1,923 cm2

D. 24,542 cm2

23. If the dimensions of a rectangle with an area of 100 cm2 are tripled, what would be the area of the new rectangle?

24. A triangle has a perimeter of 18 in. If the dimensions of the triangle are multiplied by a scale factor of ½, what is the effect on the perimeter of the triangle?

A. The new perimeter is ¼ of the original perimeter.

B. The new perimeter is ½ of the original perimeter.

C. The new perimeter is twice the original perimeter.

D. The new perimeter is 4 times the original perimeter.

25. Marco has a storage shed that measures 12 feet long, 10 feet wide and 8 feet tall. If Marco doubles each of the dimensions, how much more storage space will he have?

A. The new shed will have twice the storage space

B. The new shed will have four times the storage space

C. The new shed will have 8 times the storage space

D. The new shed will have 16 times the storage space.

26. Write the equation for the data represented in the table below in slope intercept form.

x / y
3 / 11
2 / 13
1 / 15
0 / 17
-1 / 19

27. Which equation represents the line that has a slope of -2 and passes through the point (-4, 6)?

28. What is the slope of the line represented by the line ?

29. What is the slope of the line represented below?

A. 2

B. -2

C. ½

D. -½

30. What is the equation of the line shown below?

31. Which inequality best describes the graph shown below?

32. One oyster provides approximately 17 calories. A shrimp provides approximately 26 calories. Jacob wants to consume no more than 300 calories eating oysters and shrimp. Which inequality best represents the number of oysters, x, and the number of shrimp, y, that Jay can eat and stay within this limit?

33. Which inequality best represents the graph shown below?

34. Which of the following best describes the graph of the inequality ?

A. The graph has a solid line with a negative slope that crosses the y-axis at 5, with shading above.

B. The graph has a dotted line with a negative slope that crosses the y-axis at 5 with shading above.

C. The graph has a solid line with a negative slope that crosses the y-axis at 5, with shading below.

D. The graph has a dotted line with a negative slope that crosses the y-axis at 5 with shading below.

35. Macy’s is giving a free gift to all customers that spend more than $50 on t-shirts and socks. T-shirts cost $5 each and socks cost $2 per pair. Which inequality below best represents the quantity of t-shirts and socks that must be purchased to receive the free gift? Let t represent the number of t-shirts purchased and let s represent the quantity of socks purchased.

36. Which equation is the parent function of the graph below?

37. The graph of the function is shown below.

If the graph of the original function is translated 5 units up, which of the following equations best represents the translation of each point on the curve?

38. Which statement describes what happens to the graph of when the value of a is changed from 1 to 6?

A. The graph narrows

B. The graph widens

C. The graph moves up 6 units

D. The graph moves down 6 units.

39. Which of the following is the vertex of the graph of

A. (5, -3)

B. (-3, 5)

C. (3, 5)

D. (5, 3)

40. Which points best represent the solutions of the graphed quadratic equation shown below?

A. and

B. and

C. and

D. and

41. Stephen is flying a kite with an angle of inclination of 49º. How much string must he let out if he wants the kite to be above a birdbath that is exactly 212 ft from where he is standing?

A. 253 ft

B. 565 ft

C. 139 ft

D. 323 ft

42. ∆WXY is a right triangle. Find the length of .

A. 20 mm

B. 34.64 mm

C. 60 mm

D. 69.28 mm

43. A wheelchair ramp makes a 10º angle with the ground. The length of the ramp is 25 feet; find out how high the ramp rises.

A. 4.34 ft

B. 5.75 ft

C. 143 ft

D. 24 ft

44. Jane is estimating the height of a pine tree. She is standing 75 ft from the tree and has an angle of inclination of 60o. How tall is the tree?

A. 500 ft

B. 129 ft

C. 37 ft

D. 65 ft

45. Find the area of triangle RST.

A. 16 ft2

B. 32 ft2

C. 24 ft2

D. 40 ft2

46. Find the area of sector LJK

A. 3.14 ft2

B. 0.52 ft2

C. 1.0 ft2

D. 113. 1 ft2

47. Find the arc length of

A. 25.13 ft

B. 4.18 ft

C. 8.24 ft

D. 16.76 ft

48. Find the volume of the shaded sector of the cylinder.

A. 466.53 ft3

B. 7.2 ft3

C. 57 ft3

D. 129.6 ft3

49. Find

A. 55º

B. 180º

C. 133º

D. 102º

50. Find

A. 54º

B. 5400º

C. 72º

D. 15º

51. Which ordered pair below represents the solution to the following system of equations?

A. (4, -2)

B. (0, 4)

C. (1, -1)

D. (1, 1)

52. Manuel went to Bob’s Burger Stop on Monday and bought 2 Jumbo Burgers and 3 Baby Burgers for $13.50. On Tuesday Manuel bought 4 Jumbo Burgers and 5 Baby Burgers for $25.50. What is the price for 1 Jumbo Burger and 1 Baby Burger?

A. $6.00

B. $6.50

C. $7.00

D. $7.50

53. The Austin Rodeo offers 2 different admission plans. Plan A charges $20 entrance fee, plus $1 per ride. Plan B charges $15 entry, plus $2 per ride. At how many rides to the plans have the same total cost?

A. 3 rides

B. 4 rides

C. 5 rides

D. 25 rides

54. Sally prefers Chick-Fil-A, so she goes there for lunch. Chicken Sandwiches, c, cost $1.99 and Waffle Fries, f, cost $0.89. If Sally spends $7.54 and buys a total of 6 items, what system of equations can be used to determine how many Waffle Fries she bought?

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