Do Not Write on This Test

DO NOT WRITE ON THIS TEST

Geometry Midterm 2009

DO NOT WRITE ON THIS TEST

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. A 14-foot ladder is leaning against a house so that its top touches the top of the wall. The bottom of the ladder is 8 feet away from the wall. Which of these can be used to find the height of the wall?

A. .

B. .

C. .

D. .

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

A. Acute equilateral

B. Acute isosceles

C. Right scalene

D. Right isosceles

11. Find and.

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

13. The lengths of the sides of a triangle are y, y + 1 and 7 centimeters. If the perimeter is 56 centimeters, what is the value of y?

A. 24

B. 25

C. 31

D. 32

14. 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.

15. An artist painted a triangle on her canvas that had sides of 22 in., 25 in. and 15 in. Her plan is to paint a star in the corner of the triangle with the largest angle. Where should she paint the star?

A. In the corner opposite the side that is 15 in.

B. In the corner opposite the side that is 22 in.

C. In the corner opposite the side that is 25 in.

D. In the center of the triangle.

16. Which equation is equivalent to ?

17. 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.

18. Solve the equation

19. Solve the equation

20. Stan’s solution to an equation is shown below.

Given:

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:

A. Stan’s solution is correct.

B. Stan made a mistake in Step 1

C. Stan made a mistake in Step 3

D. Stan made a mistake in Step 5

21. The length of a rectangular garden is 25 feet greater than the width, w. Which equation best describes the garden’s area, A?

A. A = 2(w + 25) + 2w

B. A = (2w)(2w)

C. A = w(w + 25)

D. A = w + 25w

22. You are painting the walls of a rectangular room. The room is 15 feet long by 10 feet wide. The height of the room is 9 feet. Which is closest to the area being painted?

A. 450 square feet

B. 190 square feet

C. 1,350 square feet

D. 441 square feet

23. 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

24. What is the area of the shaded in the figure below?

A. 150 sq. units

B. 144 sq. units

C. 60 sq. units

D. 84 sq. units

25. Find the area of the following figure:

A. 336 in2

B. 76 in2

C. 38 in2

D. 120 in2

26. The circumference of a circle is 100 meters. Which is closest to its diameter?

A. 10 meters

B. 50 meters

C. 25 meters

D. 30 meters

27. The perimeter of the following triangle is 66 inches, what is its area?

A. 126 in2

B. 342 in2

C. 171 in2

D. 63 in2

28. The perimeter of the rectangle is 120 feet. What is the area of the shaded region?

A. 400 ft2

B. 800 ft2

C. 200 ft2

D. 180 ft2

29. Which is closest to the area of the glass window? (Hint: the top portion is a semi-circle.)

A. 2700 cm2

B. 4200 cm2

C. 6450 cm2

D. 3650 cm2

30. Figure ABCD is a kite. Find the area.

A. 24 in2

B. 21 in2

C. 42 in2

D. 66 in2

31. A triangular prism is shown below.

What is the volume in cubic inches?

A. 48 in3

B. 24 in3

C. 60 in3

D. 30 in3

32. 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

33. 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.

34. Alicia made a cylindrical clay vase for her art project. If the vase has a volume of 138 cubic inches and a radius of 2 inches, which is the closest to the height of the vase?

A. 22 inches

B. 11 inches

C. 9 inches

D. 4 inches

35. The lateral surface area of a cylinder can be described as the following using a soup can as an example.

A. The top and bottom of the can only.

B. The entire surface of the can, including the label, top and bottom of the can.

C. The label only.

D. The volume inside the soup can.

36. 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

37. 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

38. The net of a rectangular prism is shown below. What is the total surface area represented by this net?

A. 114.70 cm2

B. 150.88 cm2

C. 105.00 cm2

D. 119.88 cm2

39. 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

40. Solve for y.

41. 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

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

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

A. 2

B. -2

C. ½

D. -½

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

45. Cleo buys music from the Rhapsody music service. He pays a base fee of $6.95 and then pays $.55 for every song he downloads. Which equation below best describes the total amount of Cleo’s monthly bill, t, in terms of s, the number of sings he downloads?

46. Which graph below represents the equation ?

47. What is the slope of the line that contains the points (8, 3) and (-4, 5)?

C. -6

D. 6

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

49. Which of the following graphs represents the equation ?

50. The net of a right triangular prism is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the prism to the nearest centimeter.

What is the total surface area?

A. 34.50 cm2

B. 43.25 cm2

C. 52.00 cm2

D. 60.75 cm2

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