Indiana Academic Super Bowl. Math Round Senior Division Invitational 2. A Program of the Indiana Association of School Principals

Transcription

1 Indiana Academic Super Bowl Math Round 2018 Senior Division Invitational 2 A Program of the Indiana Association of School Principals

2 Emcee: Please remind proctors that there should be a copy of the Math Probability table and Binomial distribution handout at each table for student use in the Math round

3 Students: Throughout this round we will be pronouncing mathematic symbols and concepts as spoken words. If there are any discrepancies between what is said and what you see on the screen, the screen supersedes what is spoken.

4 Emcee: Please ask Proctors to check student calculators at this time. The only calculators allowed during this competition are the following models: TI-30Xa and TI-30X IIS If someone at your table has a different model, raise your hand for a procedural official.

5 SD-I2-M-1 40 seconds In the figure, AB = 16, BC = 15, AC = 14, and DE = 9. Find BD. A. 9.4 B. 9.6 C. 9.8 D B E D A C

6 SD-I2-M-1 In the figure, AB = 16, BC = 15, AC = 14, and DE = 9. Find BD. B B. 9.6 E D A C

7 SD-I2-M-2 Given 20 seconds find adj(a). Hint: A. B. C. D.

8 SD-I2-M-2 Given find adj(a). Hint: D.

9 SD-I2-M-3 20 sec When a binomial distribution with a large n is approximated with a normal distribution, what do you use for µ and σ? A. µ = nq, σ = B. µ = np, σ = C. µ = nq, σ = npq D. µ = np, σ = npq

10 SD-I2-M-3 When a binomial distribution with a large n is approximated with a normal distribution, what do you use for µ and σ? B. µ = np, σ =

11 SD-I2-M-4 20 seconds Evaluate the integral A. B. C. D.

12 SD-I2-M-4 Evaluate the integral A.

13 SD-I2-M-5 20 seconds To which of the following problems did Julia Robinson make a significant contribution? A. revised axioms for Euclidean geometry B. Hilbert s first problem C. Hilbert s tenth problem D. field equations for general relativity

14 SD-I2-M-5 To which of the following problems did Julia Robinson make a significant contribution? C. Hilbert s tenth problem

15 SD-I2-M-6 40 sec Let and M = C + 3A 2 B. Find m 23. A B. 16 C. 82 D. 101

16 SD-I2-M-6 Let and M = C + 3A 2 B. Find m 23. B. 16

17 SD-I2-M-7 40 seconds Callie wants to measure the width of a large rock formation. She locates points A, B, C, D, and E and takes the measurements shown in yards. What is the width of the rock formation, AB? A. 94 yards B. 98 yards C. 102 yards D. 106 yards A B C D E

18 SD-I2-M-7 Callie wants to measure the width of a large rock formation. She locates points A, B, C, D, and E and takes the measurements shown in yards. What is the width of the rock formation, AB? B. 98 yards A B 40 C 63 D E

19 SD-I2-M-8 30 sec A particle moves along the x-axis with velocity given by v(t) = 3t 2 + 6t for time t>0. If the particle is at position x = 2 at time t = 0, what is the position of the particle at time t = 2? A. 16 B. 20 C. 22 D. 24

20 SD-I2-M-8 A particle moves along the x-axis with velocity given by v(t) = 3t 2 + 6t for time t>0. If the particle is at position x = 2 at time t = 0, what is the position of the particle at time t = 2? C. 22

21 SD-I2-M-9 30 seconds A basketball player has hit 75% of her free throws throughout the season. In her final game, if she shoots 8 free throws, what is the probability that she will make exactly 6 of them? Assume each free throw is independent of the others? A..679 B..750 C..275 D..312

22 SD-I2-M-9 A basketball player has hit 75% of her free throws throughout the season. In her final game, if she shoots 8 free throws, what is the probability that she will make exactly 6 of them? Assume each free throw is independent of the others? D..312

23 SD-I2-M seconds When is matrix multiplication commutative? A. When multiplying a matrix and its inverse B. when multiplying any two square matrices of the same dimensions C. when multiplying two different identity matrices D. never

24 SD-I2-M-10 When is matrix multiplication commutative? A. When multiplying a matrix and its inverse

25 SD-I2-M seconds What is the mean of the five numbers: 3A + B, 4A 2B, 6A + 5B, B 2A, and 4A + 5B? A. B. C. 3A + B D. 3A + 2B

26 SD-I2-M-11 What is the mean of the five numbers: 3A + B, 4A 2B, 6A + 5B, B 2A, and 4A + 5B? D. 3A + 2B

27 SD-I2-M seconds If the area bounded by the curve y 2 = 4x and the line y = x is rotated about the x-axis, then the volume generated is shown by which of the following? A. B. C. D.

28 SD-I2-M-12 If the area bounded by the curve y 2 = 4x and the line y = x is rotated about the x-axis, then the volume generated is shown by which of the following? D.

29 SD-I2-M seconds What is the most direct way to conclude that the triangles are similar? A. AA B. SAS C. ASA D. these triangles may NOT be similar

30 SD-I2-M-13 What is the most direct way to conclude that the triangles are similar? B. SAS

31 SD-I2-M-14 then what is f(x)? A. B. C. D.

32 SD-I2-M-14 f(x)? then what is C.

33 SD-I2-M seconds The figure shown (where duplicate numbers have been omitted), illustrates Cantor s method to show which of the following? A. the positive rationals are not countable B. the positive rationals are countable C. the positive rationals lie between countable and the continuum D. the positive rationals equal the continuum 1 1/3 1/5. 2 2/3 2/5. 3 3/2 3/5. 4 4/3 4/5. 5 5/2 5/3 5/4...

34 SD-I2-M-15 The figure shown (where duplicate numbers have been omitted), illustrates Cantor s method to show which of the following? B. the positive rationals are countable 1 1/3 1/5. 2 2/3 2/5. 3 3/2 3/5. 4 4/3 4/5. 5 5/2 5/3 5/4...

35 SD-I2-M seconds If A and B are 3x3 invertible matrices, which of the following matrices may NOT be invertible? A. AB B. BA -1 C. A+B D. B -1

36 SD-I2-M-16 If A and B are 3x3 invertible matrices, which of the following matrices may NOT be invertible? C. A+B

37 SD-I2-M seconds The eight numbers of the set: 4, 4, 6, A, B, 13, 15, and 20 are in numerical order. The MEDIAN of this set is 9. What is the mean? A. 10 B C D

38 SD-I2-M-17 The eight numbers of the set: 4, 4, 6, A, B, 13, 15, and 20 are in numerical order. The MEDIAN of this set is 9. What is the mean? A. 10

39 SD-I2-M sec If find the value of k. A. 2 B. 3 C. 4 D. 5

40 SD-I2-M-18 If find the value of k. C. 4

41 SD-I2-M seconds In the figure shown, which of the following is NOT true? A. BC 2 = DC AC B. AC BD = AB BC C. BD 2 = AD DC D. BD AC = AD DC B A D C

42 SD-I2-M-19 In the figure shown, which of the following is NOT true? D. BD AC = AD DC B A D C

43 SD-I2-M sec Solve the matrix equation: A. B. C. D.

44 SD-I2-M-20 Solve the matrix equation: B.

45 SD-I2-M sec Let [0, 1] = {reals with 0 x 1} and let S = {(x, y) 0 x 1 and 0 y 1} For each ordered pair (x, y) x has a unique decimal expansion x = 0.x 1 x 2 x 3 and y has a unique decimal expansion y = 0.y 1 y 2 y 3 Forming the number z = 0.x 1 y 1 x 2 y 2 x 3 y 3 would indicate which of the following? A. card (S) = card ([0, 1]) B. card (S) > card ([0, 1]) C. S is countable D. card (S) is larger than the continuum

46 SD-I2-M-21 Let [0, 1] = {reals with 0 x 1} and let S = {(x, y) 0 x 1 and 0 y 1} For each ordered pair (x, y) x has a unique decimal expansion x = 0.x 1 x 2 x 3 and y has a unique decimal expansion y = 0.y 1 y 2 y 3 Forming the number z = 0.x 1 y 1 x 2 y 2 x 3 y 3 would indicate which of the following? A. card (S) = card ([0, 1])

47 SD-I2-M sec Let W be a 4x3 matrix, X be a 3x2 matrix, Y be an invertible 2x2 matrix, and Z be an invertible 3x3 matrix. Which of the following products is undefined? A. WXYX T B. ZX T W T Z C. XY -1 X T W T D. WZXY

48 SD-I2-M-22 Let W be a 4x3 matrix, X be a 3x2 matrix, Y be an invertible 2x2 matrix, and Z be an invertible 3x3 matrix. Which of the following products is undefined? B. ZX T W T Z

49 SD-I2-M seconds, BC = 7, and AD = 4. If AC = x, which equation could be used to find AC? A. x 2 + 4x + 49 = 0 B. x 2 4x 49 = 0 B A C C. x 2 4x + 49 = 0 D. x 2 + 4x 49 = 0 D

50 SD-I2-M-23, BC = 7, and AD = 4. If AC = x, which equation could be used to find AC? B B. x 2 4x 49 = 0 A C D

51 SD-I2-M seconds Find the volume of the solid generated whose boundaries are given by y = 4 and y = x 2 when rotated about the x-axis. A. B. C. D.

52 SD-I2-M-24 Find the volume of the solid generated whose boundaries are given by y = 4 and y = x 2 when rotated about the x-axis. C.

53 SD-I2-M seconds Given that x is a normally distributed random variable with µ = 33 and What is P(-3 < x < 12)? A B C D..0858

54 SD-I2-M-25 Given that x is a normally distributed random variable with µ = 33 and What is P(-3 < x < 12)? C..0726

55 End of Math Round The Next Round will be English 2018 Academic Area Super Bowl Competition Tuesday, April 17, 2018