Indiana Academic Super Bowl. Math Round Coaches Practice. A Program of the Indiana Association of School Principals

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1 Indiana Academic Super Bowl Math Round 2017 Coaches Practice A Program of the Indiana Association of School Principals

2 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.

3 The only calculators allowed during this competition are the following models: TI-30Xa and TI-30X IIS

4 SD-CP-M-1 30 seconds The following series is. 1 + ½ + ¼ + 1/8 + 1/ A. indeterminate B. convergent C. divergent D. Both A and B

5 SD-CP-M-2 The series S n = 1 + ½ + ¼ + 1/8 + 1/2 n-1 is. A. bounded above B. bounded below C. unbounded D. bounded above and below

6 SD-CP-M-3 Joseph-Louis LaGrange found that the volume of a regular tetrahedron is, where a is the length of an edge. Find the area of one face of the solid. Find the total surface area of the solid.

7 SD-CP-M-4 Write the equation for the least squares regression line for the given data points. (-2, -1), (1, 1), (3, 2)

8 SD-CP-M-5 The sales (in millions) of a company are given below. Estimate the 2018 sales. X (year) Y (sales in millions)

9 SD-CP-M-6 Expand (x 2) 3

10 SD-CP-M-7 Use Pascal s Triangle of the Binomial Theorem to expand the following: (x + 3) 5

11 SD-CP-M-8 A stone bridge is to be constructed over the Seine and modeled after a parabolic arch. The bridge is constructed at a strategic military point which happens to be the widest portion of the river, 200 meters from bank to bank. If the peak of the bridge s arch is 25 meters above the river, how far above the water is the bridge s arch 65 meters from the river bank?

12 SD-CPM-9 Determine the equation of a line tangent to the given parabola at its vertex. y = x 2 + 2x + 10

13 SD-CP-M-10 Determine the equation of the line tangent to the given circle at the given point. (x + 2) 2 + (y 4) 2 = 25; (1, 8) A. y 8 = 4/3(x 1) B. y 8 = -¾(x 1) C. y 1 = 4/3(x 8) D. y 1 = -¾(x 8)

14 SD-CP-M-11 The Arc de Triomphe has two separate sized vaults. The smaller vault is meters tall and roughly 8 meters wide. The vault is created by placing a parabolic arch atop two vertical supports. If you are to estimate the legs to be meters tall, determine the focus and directrix of the arch based on the estimated width and height of the space.

15 SD-CP-M-12 Determine the center and estimate the radius of the given circle. x 2 8x + y y = 72.

16 SD-CP-M-13 An ellipse is centered on a Cartesian coordinate grid. Its domain varies from -7 to 7 inclusive, with its range covering -3 to 3 inclusive. Create an equation for this shape.

17 SD-CP-M-14 Given the following function, f (x) = 5x 4-2x how many possible positive and negative solutions exist?

18 SD-CP-M-15 Notre Dame cathedral has a vaulted ceiling measuring roughly 33.5 meters tall. How tall is it in decimeters?

19 SD-CP-M-16 There are miles in a kilometer. If the average human walks at a rate of 3.1 miles per hour, what would the average human s rate be in centimeters per second?

20 SD-CP-M-17 Given the following function f(x) = x 3 5x 2 14x + 12, what are possible x-intercepts of the graph? A. it will not cross the x-axis B. it will cross 1 time below zero C. it will cross 1 time below zero and 1 time above zero D. it will cross 1 time below zero and 2 times above zero

21 SD-CP-M-18 What type of graph is represented by the equation x 2 y 2 + 5x 4y = 56 A. parabolic B. hyperbolic C. elliptical D. circular

22 SD-CP-M-19 During the French Revolution, what units were proposed as the new standard units of measure?

23 SD-CP-M-20 During the time of the French Revolution, French mathematicians attempted the decimalization of all units, including time. This system consisted of a day where there were 10 hours in a day, with 100 minutes in an hour and 100 seconds in a minute. If your favorite television show airs at 9:00 p.m., what time would your show air under this system?

24 End of Math Round Senior Academic Super Bowl Area Contest April 18, 2017

25 SD Math Coaches Practice Answer Key: 1. B 2. A

26 SD Math Coaches Practice Answer Key: 3. Area of one face: Total surface area of the solid:

27 SD Math Coaches Practice Answer Key: 4. x y xy x N = 3 pts Slope = Y int = Y =

28 SD Math Coaches Practice Answer Key: 5.

29 SD Math Coaches Practice Answer Key: 6. (x 2) (x 2) (x 2) (x 2 4x + 4) (x 2) x 3 6x + 12x (x + 3) 0 = 1 (x + 3) 1 = 1 1 (x + 3) 2 = (x + 3) 3 = (x + 3) 4 = (x + 3) 5 = 1x 5 + 5x x x x = x x x x x + 243

30 SD Math Coaches Practice Answer Key: 8.

31 SD Math Coaches Practice Answer Key: 9.

32 SD Math Coaches Practice Answer Key: 10.

33 SD Math Coaches Practice Answer Key: 11.

34 SD Math Coaches Practice Answer Key: 12.

35 SD Math Coaches Practice Answer Key: 13.

36 SD Math Coaches Practice Answer Key: 14.

37 SD Math Coaches Practice Answer Key: 15.

38 SD Math Coaches Practice Answer Key: 16.

39 SD Math Coaches Practice Answer Key: 17. D 18.

40 SD Math Coaches Practice Answer Key:

Math Round. Any figure shown may not be drawn to scale.

Math Round. Any figure shown may not be drawn to scale. Indiana Academic Super Bowl Math Round 2019 Coaches Practice A Program of the Indiana Association of School Principals Students: Throughout this round we will be pronouncing mathematic symbols and concepts