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1 To use the Math round questions in Powerpoint format, you must have access to MathType: MathType is used to create the math questions. You can download a free 30-day trial copy of the MathType program at After the 30-day trial period, the program becomes MathType Lite. You can still use it to project the Powerpoint; you just won t be able to create any math equations after the 30 days has expired.
2 Indiana Academic Super Bowl Mathematics Round 2015 Senior Division Coaches Practice A Program of the Indiana Association of School Principals
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.
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 in 2 B in 2 C. 21 in 2 D in 2
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
6 SD-CP-M-3 Solve for x. A. 6 B. 7 C. 8 D. 9 5 x x
7 SD-CP-M-4 Given O. If m TC = 132, find m CTF. T A. 24 B. 32 C. 40 D. 48 C F
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
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
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
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
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
13 SD-CP-M-10 If d is the diameter of a circle, then πd 2 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
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
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
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
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. 189π C π A B C D 2 D. 108π
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
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
20 SD-CP-M-17 On a coordinate plane, which point would be in the exterior of the circle with equation x 2 + y 2 8x 4y + 11 = 0? A. (1, 2) B. (4, 5) C. (5, 1) D. (8, 2)
21 SD-CP-M-18 Given 2x 2 + 2y 2 4x 10y = 0, what is the y-coordinate of the center of this circle? A. 1 B. 2 C. 2 ½ D. 2 ¾
22 SD-CP-M-19 Given 3x 2 + 3y 2 6x 10y = 0, What is the approximate radius of this circle? A B C D. 1.94
23 SD-CP-M-20 Given 2x 2 + 8x + 2y 2 3y 1 = 0, what is the radius of this circle? A. 2 B. C. 4 D
24 SD-CP-M-21 Given 2x 2 + 2y 2 + 3x + 5y + 4 = 0, what is the center of this circle? A. B. 3 4, , 5 2 C. 3 D. The figure is 8, 5 4 not a circle
25 SD-CP-M-22 ABCD is a square with AB = 4. Which of the following is FALSE? A. B. C. D. CD = BA AB + BC = 2(CD BC = 4 AB + BC = 4 2
26 SD-CP-M-23 AB Given A (7, -2) and B (3, -2), find. A B C D
27 SD-CP-M-24 Find the measure of the angle between U = (3, -4) and V = (3, 4). A B C D
28 SD-CP-M-25 Given A (1, 5), B (4, 6), and C (2, 8), find the measure of A. A B C D. 53.1
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)
30 SD-CP-M-27 If 5a 11 + b = 4 2 and a + b 3 = 3, then b =. A. 2 B. 3 7 C. D. -3 2
31 SD-CP-M-28 Given y x 2 = 0 and 2x 2 + y 2 = 8, then which of the following is NOT a possible value for either x or y? A. -2 B. 2 C. D. 2 2
32 SD-CP-M-29 Given x 2 + y 2 = 4 and 2x 2 + y 2 = 5, then which of the following is NOT a possible value for either x or y? A. 0 B. 1 C. -1 D. 3
33 SD-CP-M-30 Given x 2 + y 2 = 9 and 3x 2 + y 2 = 3, then y = A. B. 3 6 C 12 D. There is no solution
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
35 SD-CP-M-32 The graph of x 2 + y = 10 and x + y = 10 intersect in two points. The distance between the two points is. A. 1 B. C. 2 3 D. 2
36 SD-CP-M-33 If 2a + 3b = 0 and 5a 2b = -19, then a =. A. -3 B. -5 C. D
37 SD-CP-M-34 If 2y = 11 3x and 5x = y, then y =. A. -3 B. -1 C. 1 D. 3
38 SD-CP-M-35 The value(s) of y for which the pair of equations x 2 + y 2 16 = 0 and x 2 3y + 12 = 0 may have a real common solution are. A. 4 B. -7, 4 C. 0, 4 D. No y
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
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
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
42 SD-CP-M-39 Given 3x + y = -9 and x 2y = 4, then x =. A. -3 B. -2 C. 0 D. 1
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
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
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
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
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
48 SD-CP-M-45 In the expression of xy 2, 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
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
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
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%
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%
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
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
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%
56 SD-CP-M-53 Due to inflation, the price of a textbook increased 5%. The new price is $ What was the original price? A. $64.70 B. $64.80 C. $64.90 D. $65.00
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
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%
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. 1 A. B. 1 p p p C. D. p 1 p p + 1
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
61 SD-CP-M-58 VIII + VII II II IV = A. XCIX B. C C. CII D. CIV
62 SD-CP-M-59 IXDCCCLXIV XII = A. DCCXXII B. DCCCXVIII C. DCCCXXXIV D. DCCCXXVIII
63 SD-CP-M-60 LXVII + CCIV = A. CCLXXI B. CCLXXXIV C. CCLXXVI D. CCLXIX
64 SD-CP-M-61 Find the mean of 211 5, 1E 12, and A B C. 2E 12 D. 37
65 SD-CP-M-62 Find MMCCIX A B C. XLV D. 3E 12
66 SD-CP-M-63 XCVII A. IVCLXXI B C D. 24E7 12
67 SD-CP-M-64 If = 4x4 8, find the value of x. A. 0 B. 2 C. 4 D. 6
68 SD-CP-M-65 XXVIII IX = A. CCLXXII B C. 18X 12 D
69 SD-CP-M A B C D. XXIX
70 SD-CP-M-67 If 31a 8 = 14X 12, find the value of a. A. 2 B. 4 C. 6 D. Cannot be determined
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
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
73 SD-CP-M = A B C D
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
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
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
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
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
79 SD-CP-M-76 Which mathematician is a key figure in the development of trigonometry? A. Archimedes B. Heron C. Menelaus D. Pappus
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
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
82 End of Math Round Senior Super Bowl Area Contest - April 21, 2015
83 SD Math Coaches Practice Answer Key: 1. A 11. D 21. A 31. D 41. A 51. A 61. D 71. A 2. A 12. C 22. B 32. B 42. A 52. C 62. D 72. A 3. A 13. B 23. B 33. A 43. D 53. C 63. B 73. D 4. A 14. B 24. A 34. C 44. B 54. B 64. D 74. D 5. D 15. B 25. D 35. A 45. D 55. B 65. B 75. B 6. B 16. C 26. C 36. D 46. C 56. D 66. B 76. C 7. B 17. D 27. B 37. C 47. D 57. C 67. A 77. D 8. B 18. C 28. A 38. A 48. C 58. C 68. C 78. B 9. D 19. D 29. A 39. B 49. A 59. A 69. C 10. D 20. B 30. D 40. C 50. C 60. A 70. D
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