Page 1
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Page 2
Indiana Academic Super Bowl
A Program of the Indiana Association of School Principals
Mathematics Round2015 – Senior Division Coaches Practice
Page 3
Students:
Throughout this competition, foreign
names and words may be used.
If there are any discrepancies
between how a word/phrase should
be pronounced and what you see
on the screen, the screen
supersedes what is spoken.
Page 4
SD-CP-M-1
A central angle of 60° is plotted on a circle
with a radius of 12 inches. Calculate the
area of the circular segment between the
chord joining the ends of the two radii and
its corresponding arc.
A. 13 in2
B. 16.5 in2
C. 21 in2
D. 24.5 in2
Page 5
SD-CP-M-2
Two circles in the same plane cannot
have the following number of common
tangents:
A. 1
B. 2
C. 3
D. 4
Page 6
SD-CP-M-3
Solve for x.
A. 6
B. 7
C. 8
D. 9
5x + 1
8.4
x
Page 7
SD-CP-M-4
A. 24
B. 32
C. 40
D. 48
T
C F
Given ⊙O. If 𝑚 𝑇𝐶 = 132∘, find 𝑚∠𝐶𝑇𝐹.
Page 8
SD-CP-M-5
Triangle ABC is inscribed in a circle. The
measure of the non-overlapping minor arcs
AB, BC, and CA are, respectively, x + 75°,
2x + 25°, and 3x – 22°. Then one interior
angle of the triangle is ___________.
A. 57°
B. 59°
C. 60°
D. 61°
Page 9
SD-CP-M-6
A circle has a radius of 12 units. What is
the length of a minor arc formed by a
central angle of 120°?
A.4π
B.8π
C.16π
D.24π
Page 10
SD-CP-M-7
Concentric circles have radii of 4” and
6”. If a central angle cuts off an arc of
4” on the circle with the 4” radius, then
the length of the arc it will cut off on the
circle with a 6” radius is _________.
A. 4”
B. 6”
C. 8”
D. 9”
Page 11
SD-CP-M-8
Circle I is circumscribed about a given
square and Circle II is inscribed in the given
square. If r is the ratio of the area of Circle I
to that of Circle II, then r equals ________.
A.
B. 2
C.
D. 8
Page 12
SD-CP-M-9
If the radius of a circle were increased
by 2 inches, the area would be
increased by 32π square inches. What
is the radius?
A.4 inches
B.5 inches
C.6 inches
D.7 inches
Page 13
SD-CP-M-10
If d is the diameter of a circle, then
πd2 represents _______.
A. the area of the circle
B. half the area of the circle
C. one-fourth the area of the circle
D. four times the area of the circle
Page 14
SD-CP-M-11
The number of circular pipes with an
inside diameter of 1 inch which will
carry the same amount of water as a
pipe with an inside diameter of 6 inches
is _________.
A. 6π
B. 6
C. 36π
D. 36
Page 15
SD-CP-M-12
The radii of two circles are in the ratio
2 to 3. If the area of the larger circle is 54π,
find the area of the smaller circle.
A. 6π
B. 18π
C. 24π
D. 36π
Page 16
SD-CP-M-13
If the circle with center A has an area of
72π, what is the area of the circle with
center B?
A.12π
B.18π
C.24π
D.30π
A B
Page 17
SD-CP-M-14
Each of the three shaded areas is a semicircle.
If AB = 6, CD = 2BC and BC = 2AB, then the
area of the entire shaded figure is ____.
A. 90π
B.
C.
D. 108π
189𝜋
2
203𝜋
2
ADB
C
Page 18
SD-CP-M-15
If the area of a circle is 64π, then the
circumference of the circle is _____.
A. 8π
B.16π
C.32π
D.64π
Page 19
SD-CP-M-16
If the radius of a circle is increased by 1
unit, the ratio of the new circumference
to the new diameter is _______.
A. π + 2
B. π (r + 1)
C. π
D. 2π
Page 20
SD-CP-M-17
On a coordinate plane, which point would be
in the exterior of the circle with equation
x2 + y2 – 8x – 4y + 11 = 0?
A. (1, 2)
B. (4, 5)
C. (5, 1)
D. (8, 2)
Page 21
SD-CP-M-18
Given 2x2 + 2y2 – 4x – 10y = 0,
what is the y-coordinate of the
center of this circle?
A. 1
B. 2
C. 2 ½
D. 2 ¾
Page 22
SD-CP-M-19
Given 3x2 + 3y2 – 6x – 10y = 0,
What is the approximate radius of
this circle?
A. 1.68
B. 1.71
C. 1.76
D. 1.94
Page 23
SD-CP-M-20
Given 2x2 + 8x + 2y2 – 3y – 1 = 0,
what is the radius of this circle?
A. 2 B.
C. 4 D.
9
4
9
2
Page 24
SD-CP-M-21
Given 2x2 + 2y2 + 3x + 5y + 4 = 0,
what is the center of this circle?
A. B.
C. D. The figure is
not a circle
−3
4, −5
4
3
8, −5
2
−3
8,5
4
Page 25
SD-CP-M-22
ABCD is a square with
Which of the following is FALSE?
A.
B.
C.
D.
|𝐴𝐵| = 4.
𝐶𝐷 = 𝐵𝐴
𝐴𝐵 + 𝐵𝐶 = 2(𝐶𝐷
|𝐵𝐶| = 4
|𝐴𝐵 + 𝐵𝐶| = 4 2
Page 26
SD-CP-M-23
Given A (7, -2) and B (3, -2), find .
A. 3.47
B. 4.00
C. 7.28
D. 10.89
|𝐴𝐵 |
Page 27
SD-CP-M-24
Find the measure of the angle between
U = (3, -4) and V = (3, 4).
A. 106.3°
B. 111.5°
C. 126.8°
D. 134.4°
Page 28
SD-CP-M-25
Given A (1, 5), B (4, 6), and
C (2, 8), find the measure of A.
A. 18.4°
B. 26.8°
C. 39.2°
D. 53.1°
∠
Page 29
SD-CP-M-26
Find the coordinates of the vertices of the
triangle with sides determined by the graphs:
4x + 3y + 1 = 0
4x – 3y – 17 = 0
4x – 9y + 13 = 0
Which of the following is NOT a vertex?
A. (2, -3) B. (-1, 1)
C. (5, 2) D. (8, 5)
Page 30
SD-CP-M-27
If
then b = __________.
A. 2 B. 3
C. D. -3
5𝑎
4+ 𝑏 =
11
2 and 𝑎 +
𝑏
3= 3,
7
2
Page 31
SD-CP-M-28
Given y – x2 = 0 and 2x2 + y2 = 8, then which of
the following is NOT a possible value for either x
or y?
A. -2
B. 2
C.
D.
− 2
2
Page 32
SD-CP-M-29
Given x2 + y2 = 4 and 2x2 + y2 = 5, then
which of the following is NOT a
possible value for either x or y?
A. 0
B. 1
C. -1
D. − 3
Page 33
SD-CP-M-30
Given x2 + y2 = 9 and 3x2 + y2 = 3, then y =
A.
B.
C
D. There is no solution
3
6
12
Page 34
SD-CP-M-31
Given x + y + z = 6
2x – y + z = 3
x – y + 2z = 5,
the sum of the solutions is _________.
A. -4
B. 0
C. 3
D. 6
Page 35
SD-CP-M-32
The graph of x2 + y = 10 and x + y =
10 intersect in two points. The
distance between the two points is
______.
A. 1
B.
C.
D. 2
2
3
Page 36
SD-CP-M-33
If 2a + 3b = 0 and 5a – 2b = -19, then
a = ___________.
A. -3
B. -5
C. D. 2−57
11
Page 37
SD-CP-M-34
If 2y = 11 – 3x and 5x = 11 + 4y, then y = ________.
A. -3
B. -1
C. 1
D. 3
Page 38
SD-CP-M-35
The value(s) of y for which the pair of equations x2 + y2 – 16 = 0 and
x2 – 3y + 12 = 0 may have a real common solution are ______.
A. 4
B. -7, 4
C. 0, 4
D. No y
Page 39
SD-CP-M-36
Given a system of one straight line and
one parabola, the solution set may NOT
be ____________.
A. One point
B. Two points
C. No points
D. Infinitely many points
Page 40
SD-CP-M-37
Find the value of k if (-2, 4) is the solution for the system of equations
3x + ky = 18 and 5x + 2 ky = 38.
A. 4
B. 5
C. 6
D. 7
Page 41
SD-CP-M-38
Given x - y + z = 8
5x + 4y – z = 7
2x + y – 3z = -7
the sum of the solutions is _________.
A. 6
B. 8
C. 8
D. 12
Page 42
SD-CP-M-39
Given 3x + y = -9 and x – 2y = 4, then x = _____.
A. -3
B. -2
C. 0
D. 1
Page 43
SD-CP-M-40
Given two linear equations, the solution
set may NOT be __________.
A. No points
B. One point
C. Two points
D. Infinitely many points
Page 44
SD-CP-M-41
A certain fishing spot is located 45 kilometers
from town. Part of the distance can be driven, but
part of it must be traveled on foot. It if is possible
to drive 19 more kilometers than must be walked,
how far must be walked?
A. 13
B. 16
C. 19
D. 22
Page 45
SD-CP-M-42
A 30-meter board is cut into two pieces,
one of which is 6 meters shorter than the
other. How long, in meters, is the
shorter piece?
A. 12
B. 14
C. 16
D. 18
Page 46
SD-CP-M-43
The sum of two numbers is 25 and their
difference is 9. What is the larger
number?
A. 8
B. 11
C. 14
D. 17
Page 47
SD-CP-M-44
The sum of three numbers is 58. Twice the first
number added to the sum of the second and third
numbers is 71. If the first number is added to four
times the second number and the sum is decreased
by three times the third number, the result is 18.
Which of the following is NOT one of the
numbers?
A. 13
B. 15
C. 20
D. 25
Page 48
SD-CP-M-45
In the expression of xy2, the value of x and y
are each decreased by 25%. Therefore, the
value of the expression is ______.
A. 50% of the original value
B. 9/16 of the original value
C. 75% of the original value
D. 27/64 of the original value
Page 49
SD-CP-M-46
Applied to a bill of $10,000, the difference
between a discount of 40% and two
successive discounts of 36% and 4%,
expressed in dollars is _______.
A. $0
B. $72
C. $144
D. $256
Page 50
SD-CP-M-47
Paul receives a weekly salary of $80 plus a
commission of 2% on sales over $2000 and an
additional 1% of sales over $11,000. If his total
sales were $13,500 for the week, how much did he
earn?
A. $210
B. $315
C. $285
D. $335
Page 51
SD-CP-M-48
Successive discounts of 10% and 20% are
equivalent to a single discount of _____.
A. 15%
B. 25%
C. 28%
D. 30%
Page 52
SD-CP-M-49
If a dealer could get his goods for 8% less
while keeping his selling price fixed, his
profit, based on costs, would be increased
to (x + 10)% from his present profit of x%,
which is?
A. 15%
B. 14%
C. 13%
D. 12%
Page 53
SD-CP-M-50
The ratio of 3 ¼ to 5 ¼ is equivalent to
the ratio of ___________.
A. 3 to 5
B. 5 to 3
C. 13 to 21
D. 5 to 7
Page 54
SD-CP-M-51
In a local election, votes were cast for Mr.
Dyer, Ms. Frau, and Mr. Borak in the ratio
of 4:3:2. If there were no other candidates
and none of the 1800 voters cast more than
one vote, how many votes did Ms. Frau
receive?
A. 600
B. 650
C. 730
D. 800
Page 55
SD-CP-M-52
A stock decreases in value by 20%. By what
percent must the stock price increase to
reach its former value?
A. 20%
B. 23%
C. 25%
D. 30%
Page 56
SD-CP-M-53
Due to inflation, the price of a textbook
increased 5%. The new price is $68.14.
What was the original price?
A. $64.70
B. $64.80
C. $64.90
D. $65.00
Page 57
SD-CP-M-54
A man bought 10 crates of oranges for a total
cost of $80. If 2 of the crates went bad and
were not sellable, at what price would he have
to sell each of the remaining crates in order to
earn a total profit of 25% of his total cost?
A. $10
B. $12.50
C. $15
D. $17.50
Page 58
SD-CP-M-55
A chemist wishes to make 9 liters of a 30%
acid solution by mixing 3 solutions of 5%,
20%, and 50%. How much of each solution
must the chemist use if twice as much 50%
solution is used than 5% solution?
A. 1l 5%, 1l 20%, 2l 50%
B. 2l 5%, 3l 20%, 4l 50%
C. 3l 5%, 4l 20%, 6l 50%
D. 4l 5%, 6l 20%, 8l 50%
Page 59
SD-CP-M-56
If the price of an article is increased by
percent p, then the decrease in percent
of sales must not exceed d in order to
yield the same income. The value of d
is ________.
A. B.
C. D.
1
1 − 𝑝
1
1 + 𝑝
𝑝
𝑝 + 1
𝑝
𝑝 − 1
Page 60
SD-CP-M-57
Which of the following is not a proper way
to write a Roman numeral?
A. MDCLXVI
B. LXXXVIII
C. DICLXVII
D. DCCXXVV
Page 61
SD-CP-M-58
A. XCIX
B. C
C. CII
D. CIV
VIII + VIIII • II – IV =
Page 62
SD-CP-M-59
A. DCCXXII
B. DCCCXVIII
C. DCCCXXXIV
D. DCCCXXVIII
𝐼𝑋𝐷𝐶𝐶𝐶𝐿𝑋𝐼𝑉 ÷ 𝑋𝐼𝐼 =
Page 63
SD-CP-M-60
LXVII + CCIV =
A. CCLXXI
B. CCLXXXIV
C. CCLXXVI
D. CCLXIX
Page 64
SD-CP-M-61
Find the mean of 2115, 1E12, and
408.
A. 1215
B. 448
C. 2E12
D. 37
Page 65
SD-CP-M-62
Find
A. 1335
B. 618
C. XLV
D. 3E12
𝑀𝑀𝐶𝐶𝐼𝑋
Page 66
SD-CP-M-63
A.
B. 1131315
C. 101138
D. 24E712
𝑋𝐶𝑉𝐼𝐼 • 3712 ≠
𝐼𝑉𝐶𝐿𝑋𝑋𝐼
Page 67
SD-CP-M-64
If 21812 = 4x48, find the value of
x.
A. 0
B. 2
C. 4
D. 6
Page 68
SD-CP-M-65
A. CCLXXII
B. 3748
C. 18X12
D. 22045
XXVIII • IX =
Page 69
SD-CP-M-66
3712 – 2 • 42 + 1612 ≠
A. 1045
B. 338
C. 2512
D. XXIX
Page 70
SD-CP-M-67
If 31a8 = 14X12, find the value of a.
A. 2
B. 4
C. 6
D. Cannot be determined
Page 71
SD-CP-M-68
A bar placed on top of a digit in a
Roman numeral increases the
number by a factor of _________.
A. 10
B. 100
C. 1,000
D. 10,000
Page 72
SD-CP-M-69
The number 10! (in base 10) when
written in base 12 ends with
exactly how many zeroes?
A. 2
B. 3
C. 4
D. 5
Page 73
SD-CP-M-70
A. 12415
B. 12335
C. 13035
D. 13015
1015 + 125 • 335 − 245 =
Page 74
SD-CP-M-71
Which mathematician gave birth to the calculus
of the infinite conceived and brought to perfection
by Kepler, Cavalieri, Fermat, Leibniz, and
Newton?
A. Archimedes
B. Heron
C. Pappus
D. Ptolemy
Page 75
SD-CP-M-72
Which mathematician, considered by
most to be the greatest mathematician of
antiquity, used the method of exhaustion
to calculate the area under the arc of a
parabola?
A.Archimedes
B. Heron
C. Ptolemy
D.Menelaus
Page 76
SD-CP-M-73
Which mathematician wrote The
Geography, an attempt to summarize
the geographical knowledge of the
habitable world as known at that time?
A. Archimedes
B. Heron
C. Pappus
D. Ptolemy
Page 77
SD-CP-M-74
Who wrote the Almagest, the
supreme authority on astronomy
until Copernicus’s publications?
A. Archimedes
B. Heron
C. Pappus
D. Ptolemy
Page 78
SD-CP-M-75
Which mathematician extended and
generalized the Pythagorean theorem,
applying it to all triangles, whether right
triangles or not?
A. Archimedes
B. Pappus
C. Menelaus
D. Heron
Page 79
SD-CP-M-76
Which mathematician is a key figure
in the development of trigonometry?
A. Archimedes
B. Heron
C. Menelaus
D. Pappus
Page 80
SD-CP-M-77
Which of the following mathematicians
was not a member of the Museum in
Alexandria, where the study of
mathematics flourished with remarkable
success?
A. Archimedes
B. Pappus
C. Ptolemy
D. Menelaus
Page 81
SD-CP-M-78
Which mathematician developed a
formula for finding the area of a triangle
from its side lengths?
A. Archimedes
B. Heron
C. Pappus
D. Ptolemy
Page 82
End of Math Round
Senior Super Bowl Area Contest - April 21, 2015
Page 83
SD Math Coaches Practice Answer Key:
1. A
2. A
3. A
4. A
5. D
6. B
7. B
8. B
9. D
10. D
11. D
12. C
13. B
14. B
15. B
16. C
17. D
18. C
19. D
20. B
21. A
22. B
23. B
24. A
25. D
26. C
27. B
28. A
29. A
30. D
31. D
32. B
33. A
34. C
35. A
36. D
37. C
38. A
39. B
40. C
41. A
42. A
43. D
44. B
45. D
46. C
47. D
48. C
49. A
50. C
51. A
52. C
53. C
54. B
55. B
56. D
57. C
58. C
59. A
60. A
61. D
62. D
63. B
64. D
65. B
66. B
67. A
68. C
69. C
70. D
71. A
72. A
73. D
74. D
75. B
76. C
77. D
78. B