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Indiana Academic Super Bowl
Mathematics Round
2009 Senior Division Coaches Practice
A Program of the Indiana Association of School
Principals
3
SD-CP-M-1

• Simplify
• a.
• b.
• c.
• d.

4
SD-CP-M-2

• Suppose an object moves in a straight line so
  that
• after t seconds, it is from its starting
• point. Find the distance the object travels
  between the times t 2 and t x.
• a. b.
• c. d.

5
SD-CP-M-3

• The area of a rectangle is square feet and the
  length is ft. What is the width
• of the rectangle?
• a. 3x 4 b. 4x 3
• c. 3x 4 d. 4x - 3

6
SD-CP-M-4

• The base of a rectangular box has length 2x 3
  feet and width x 2 feet. If the height of the
  box is x 1 feet, find the volume of the box.
• a. b.
• c. d.

7
SD-CP-M-5

• Which of the following is a term of the product
  of
• a. 27x2
• b. 14x3
• c. -21x
• d. 70

8
SD-CP-M-6

• Which of the following is NOT a term of the sum
  of ?
• a. -5x
• b. -9
• c. 3x2
• d. 12x3

9
SD-CP-M-7

• Which of the following is a term of the
  difference of
• a. b.
• c. d.

10
SD-CP-M-8

• Factor completely.
• a. b.
• c. d.

11
SD-CP-M-9

• What are the factors of
• a. (x 2) (x 1) (x 1)
• b. (x 2) (x 1) (x 1)
• c. (x 2) (x2 1)
• d. (x2 2) (x 1)

12
SD-CP-M-10

• If y x - 3, find the value of y2 y 6.
• a. b.
• c. d.

13
SD-CP-M-11

• Which binomial is a factor of
• a. x 3
• b. x 3
• c. x 1
• d. x - 1

14
SD-CP-M-12

• Simplify
• a. b.
• c. d.

15
SD-CP-M-13

• Simplify
• a. b. x
• c. d. -x

16
SD-CP-M-14

• If m n 5 and m n 9, then m2 n2 ____?
• a. 14
• b. 25
• c. 28
• d. 45

17
SD-CP-M-15

• The cost of one hamburger and two large sodas is
  5.40. The cost of three hamburgers and one
  large soda is 8.70. What is the cost of one
  hamburger?
• a. 1.65
• b. 1.90
• c. 2.40
• d. 2.60

18
SD-CP-M-16

• Solve the system of equations y 2 x
• y x2
• a. There is no solution
• b. (-1, 1) (2, 4)
• c. (1, 1) (-2, 4)
• d. (1, 1) (2, 4)

19
SD-CP-M-17

• How many solutions does the system of equations
• have x2 y2 25
• 9x2 y2 25
• a. one
• b. two
• c. three
• d. four

20
SD-CP-M-18

• Solve the system x2 y2 25
• x y2 -13
• a. (3, -4)
• b. (3, -4) (-4, 3)
• c. (3, -4) (-4, 3) (-4, -3)
• d. (3, -4) (3, 4) (-4, 3) (-4, -3)

21
SD-CP-M-19

• If 2x 4y 13 and x y -1, find x y.
• a. 0
• b. 2
• c. 4
• d. 6

22
SD-CP-M-20

• Given the right triangle with lengths of sides as
• shown, find h.
• a. 2.94
• b. 4.53
• c. 5.82
• d. 6.95

8.3
5.4
h
9.9
23
SD-CP-M-21

• If , find CB.
• a. 10 b.
• c. 6 d.

C
6
4
M
N
8
8
B
A
24
SD-CP-M-22

• bisects
• a. 15.5
• b. 19
• c. 24.5
• d. 28

B
12
D
x - 5
32
A
C
2x - 3
25
SD-CP-M-23

• bisects
• a. 10.05
• b. 9.82
• c. 9.04
• d. 8.18

B
12
10
A
C
D
x
18
26
SD-CP-M-24

• If MNPQ is a parallelogram, find RN.
• a.
• b. 20
• c.
• d. 40

R
30
S
Q
P
20
M
50
N
27
SD-CP-M-25

• At the same time a tree casts a 450 shadow, a
• 54 person casts an 84 shadow. How tall is the
  tree?
• a. 27 ¾ ft.
• b. 343 in.
• c. 24 1/12 ft.
• d. 306 in.

28
SD-CP-M-26

• Solve for x.
• a. 16
• b. 32
• c. 48
• d. 64

D
10
x
A
E
F
12
5
32
C
B
6
29
SD-CP-M-27

• Which of the following is NOT a valid similarity
• theorem?
• a. SSA
• b. SSS
• c. AA
• d. SAS

30
SD-CP-M-28

• The area of a square is 18. What is the longest
• straight line that can be drawn between any two
• points of the square?
• a. 12
• b. 6
• c.
• d.

31
SD-CP-M-29

• The floor of a rectangular room measures 6 meters
  along one wall and 7 meters along the adjacent
  wall. What is the distance in meters from one
  corner of the floor to the far corner of the
  floor?
• a.
• b. 9.1
• c. 9
• d. 8

32
SD-CP-M-30

• Which of the following could represent the
  measures of the sides of a right triangle?
• a. 20, 21, 28
• b. 37, 12, 34
• c. 7, 23, 24
• d. 4, 7.5, 8.5

33
SD-CP-M-31

• Given this figure, which statement is true?
• a. b.
• c. d. none are true

b
y
a
x
34
SD-CP-M-32

• What is the geometric mean of 5 and 15?
• a.
• b. 7.5
• c. 10
• d.

35
SD-CP-M-33

• Given right with altitude , solve
• for x.
• a. 4.2
• b. 4.5
• c. 4.7
• d. 5.1

B
x
A
C
9
D
2
36
SD-CP-M-34

• Given right , with measures as shown,
  solve for x.
• a. 2.5
• b. 3.7
• c. 3.8
• d. 4.4

B
6.2
A
C
8.7
x
37
SD-CP-M-35

• What is the geometric mean of 8 and 20?
• a. 14
• b.
• c.
• d. 2.5

38
SD-CP-M-36

• What is the volume of a right cone if its slant
  height is 17 ft. and its radius is 11 ft.?
• a. 587.5 ft.3
• b. 1013.7 ft.3
• c. 1642.4 ft.3
• d. 2154.1 ft.3

39
SD-CP-M-37

• Find the surface area, in square inches, of a
• rectangular prism whose length is 9 in., width is
• 5 in., and height is 3 inches.
• a. 135
• b. 144
• c. 174
• d. 190

40
SD-CP-M-38

• What is the surface area of a cube whose volume
  is 216 ft3?
• a. 144 ft2
• b. 216 ft2
• c. 224 ft2
• d. 228 ft2

41
SD-CP-M-39 30 seconds

• To the nearest square inch, find the lateral
  area.
• a. 144
• b. 310
• c. 340
• d. 360

12 in.
9 in.
10 in.
4 in.
7 in.
8 in.
42
SD-CP-M-40

• What is the volume of a right cone if the height
  is 10.8 m and the radius is 6 m?
• a. 396.6 m3
• b. 407.2 m3
• c. 916.4 m3
• d. 1221.5 m3

43
SD-CP-M-41

• Sphere A has a volume of .
  Sphere B
• has an area of . Which sphere
  has the
• larger radius?
• a. Sphere A
• b. Sphere B
• c. They are the same
• d. Not enough information

44
SD-CP-M-42

• A rectangular swimming pool is 22 ft. long by
• 18 ft. wide and has a constant depth of 4 ft.
  How
• many gallons of water will the pool hold if there
• are 7 ½ gallons per cubic foot?
• a. 1584 gallons
• b. 2112 gallons
• c. 9824 gallons
• d. 11880 gallons

45
SD-CP-M-43

• Acme, Inc. makes a storage container that is 10
  ft.
• wide, 25 ft. long, and 8 ft. high If they design
  a new container which increases the width and
  height by 50, how many cubic feet larger in
  volume is the new container compared to the
  original one?
• a. 3000
• b. 2500
• c. 4500
• d. 1000

46
SD-CP-M-44

• A regular hexagonal prism has a base with sides
• of length 4m and a prism height of 11m. Find the
• lateral area, in square meters.
• a. 220
• b. 244
• c. 264
• d. 352

47
SD-CP-M-45 30 seconds

• A regular pentagonal pyramid has a base with
• sides of length 18 inches, an apothem of 12.4
  inches, and a slant height of 24 inches. Find
• the surface area of the pyramid, in square
  inches.
• a. 1170
• b. 1638
• c. 2045.2
• d. 2678.4

48
SD-CP-M-46

• Find the surface area, in square centimeters.
• a. 115
• b. 120
• c. 132
• d. 135

3 cm
10 cm
5 cm
49
SD-CP-M-47

• If the volume of a cube is 27x6, what is the area
• of a face of that cube?
• a. 3x2
• b. 9x2
• c. 6x4
• d. 9x4

50
SD-CP-M-48

• Kristin is flying a kite. She has let out 60 ft.
  of
• string. If the string makes a 35 angle with the
• ground, how high above the ground is the kite?
• (Kristin is 5 ft. tall and holds the kite string
  at head height.)
• a. 39.4 ft.
• b. 42.0 ft.
• c. 47.0 ft.
• d. 49.1 ft.

51
SD-CP-M-49

• A trolley car track rises vertically 40 ft. over
  a
• horizontal distance of 650 ft. What is the angle
  of
• elevation of the track?
• a. 1.7
• b. 2.8
• c. 3.5
• d. 4.1

52
SD-CP-M-50

• In right triangle ABC with right angle at C,
• a 44 and find b.
• a. 43.6
• b. 43.7
• c. 43.8
• d. 43.9

53
SD-CP-M-51

• In and side
• t 4 units. Find the length of side m.
• a. 1.8
• b. 2.3
• c. 2.7
• d. 2.9

54
SD-CP-M-52

• A regular 12-sided polygon is inscribed in a
  circle
• whose radius is 4 in. Find the length of each
  side
• of the polygon.
• a. 1.04 in.
• b. 2 in.
• c. 2.07 in.
• d. 4 in.

55
SD-CP-M-53

• In , find a.
• a. 1.1
• b. 1.3
• c. 1.5
• d. 1.7

56
SD-CP-M-54

• In
• and . Find side q.
• a. 6.5
• b. 6.8
• c. 7.1
• d. 7.4

57
SD-CP-M-55

• Two adjacent sides of a parallelogram are 26 cm
• and 32 cm long. What is the length of the
  shorter
• diagonal if the smaller angle formed by the sides
• is 65?
• a. 31.2
• b. 31.6
• c. 32
• d. 32.4

58
SD-CP-M-56

• The given information defines how many triangles?
  A 29 a 8 c 12
• a. 0
• b. 1
• c. 2
• d. undefined

59
SD-CP-M-57

• In a 8 in., b 9 ½ in. and c
  7 ½ in.
• Find the area of in square inches.
• a. 29
• b. 32.4
• c. 35.6
• d. 38

60
SD-CP-M-58

• In
• Find the area of the triangle.
• a. 126.5 in2
• b. 147.3 in2
• c. 169.9 in2
• d. 181.7 in2

61
SD-CP-M-59

• Which of the following statements is false?
• a. The sum of the sides of a convex spherical
• triangle is always less than 360.
• b. The sum of the vertex angles of a spherical
• triangle is always larger than 180.
• c. A spherical triangle can have, at most, one
• right angle.
• d. If two sides of a spherical triangle are
  equal,
• the angles opposite these sides are equal.

62
SD-CP-M-60

• The spherical triangle ABC lies in a sphere of
• radius 12 inches. If the angles of this triangle
  have measures of 105, 85 and 80, what is the
  area of the triangle?
• a. b.
• c. d.

63
SD-CP-M-61

• The spherical triangle ABC lies in a sphere of
• radius 8 inches. If the angles of this triangle
  have
• measures of 100, 85, and 75, what is the area
• of the triangle?
• a. 89.4 sq. in.
• b. 200.9 sq. in.
• c. 312.8 sq. in.
• d. 320 sq. in.

64
SD-CP-M-62 40 seconds

• In right spherical triangle ABC, with C as the
• right angle, a 3831 and b 7819, find c to
• the nearest minute.
• a. 8053
• b. 8214
• c. 8723
• d. 9238

65
SD-CP-M-63

• Which is NOT a correct relationship for every
• right spherical triangle?
• a. sin a sin A sin c
• b. sin b sin B sin c
• c. cos b cos B sin A
• d. cos c cos b cos a

66
SD-CP-M-64

• In right spherical triangle ABC, with C as the
  right
• angle, a 119 and B 29, find side c to the
  nearest degree.
• a. 64
• b. 99
• c. 103
• d. 116

67
SD-CP-M-65 40 seconds

• In right spherical triangle ABC, with C as the
  right
• angle, a 1613 and b 597, find c to the
  nearest minute.
• a. 6028
• b. 6417
• c. 6619
• d. 6826

68
SD-CP-M-66 40 seconds

• In right spherical triangle ABC, with C as the
• right angle, a 50 and b 37, find c to the
  nearest degree.
• a. 56
• b. 59
• c. 62
• d. 65

69
SD-CP-M-67

• Using Napiers circle for right spherical
  triangles,
• which trig ratio would correctly fill in the
  blank
• in the equation cos c __________ cos a?
• a. cos b
• b. sin B
• c. sin b
• d. tan B

70
SD-CP-M-68 30 seconds

• In spherical triangle ABC,
• find side c to the nearest minute.
• a. 3940
• b. 4652
• c. 5713
• d. 6011

71
SD-CP-M-69 40 seconds

• In spherical triangle ABC,
• Find side c to the nearest degree.
• a. 71
• b. 92
• c. 100
• d. 109

72
SD-CP-M-70

• In spherical triangle ABC,
• What is the measure of side c?
• a. 85
• b. 88
• c. 93
• d. 101

73
End of Math Round
Senior Super Bowl Area Contest - April 21, 2009
74
SD Math Coaches Practice Answer Key
1. D 2. B 3. D 4. B 5. A 6. A 7.
C 8. C 9. B 10. A
11. C 12. A 13. D 14. D 15. C 16.
C 17. B 18. D 19. C 20. B
21. B 22. D 23. D 24. C 25. B 26.
B 27. A 28. B 29. A 30. D
31. C 32. A 33. C 34. D 35. C 36.
C 37. C 38. B 39. D 40. B
41. B 42. D 43. B 44. C 45. B 46.
C 47. D 48. A 49. C 50. A
51. C 52. C 53. A 54. A 55. B 56.
C 57. A 58. A 59. C 60. C
61. A 62. A 63. C 64. D 65. A 66.
B 67. A 68. A 69. D 70. A