Furman University Wylie Mathematics Tournament Ciphering Competition. March 10, 2007

Size: px

Start display at page:

Download "Furman University Wylie Mathematics Tournament Ciphering Competition. March 10, 2007"

Marcia Horton
5 years ago
Views:

1 Furman University Wylie Mathematics Tournament Ciphering Competition March 10, 2007

2 House Rules 1. All answers are integers(!) 2. All answers must be written in standard form. For example, 8 not 2 3, and 10, not ( 5 2). 1. All answers are integers(!) 2. All answers must be written in standard form. For example, 8 not 2 3, and 10, not ( 5 2).

3 Division II Round I Ciphering Participants in Round I ciphering from Division II schools should now make their way to the front.

4 Division II Round I Number 1 What is the coefficient of the term involving x 4 y 3 in the expansion of (3x 2 2y) 5?

5 Division II Round I Number 2 The function f(x) = x 2 + 5x has range {x : x k} for an integer k. What is k?

6 Division II Round I Number 3 If cos(x) = 5 13 what is 144 cot2 (x)?

7 Division II Round I Number 4 Find a positive value x such that the distance between (x, 3) and (2, 1) is 5.

8 Division II Round I Number 5 The sum of two numbers is 15 while their ratio is 1.5:1. What is their product?

9 Division II Round I Number 6 What is the area in the first quadrant bounded by the x-axis and the lines 4x + 8y = 16 and 2x + y = 2?

10 Division II Round I Number 7 Of the nine contestants in a contest, three will receive black VW Beetles, three will receive Sony plasma TV sets, and three will receive 20 gigabyte video ipods. In how many different ways can the prizes be awarded?

11 Division II Round II Ciphering Participants in Round II ciphering from Division II schools should now make their way to the front.

12 Division II Round II Number 1 Bob s age is 4 more than 3 times John s age. If their combined age is 100, how old is Bob?

13 Division II Round II Number 2 A person playing a certain lottery can win $100, $10, $1, break even or can lose $10. The probability of winning the $100 is 1/50. The probability of losing $10 is 1/2. The other options are equally likely. If the probability the person plays the lottery and finishes with more money than he or she started with is k/100, what is k?

14 Division II Round II Number 3 If (x, y) represents the coordinates of the midpoint between ( 5, 3) and (9, 3), what is xy 14 + y2 x 2 y? 7

15 Division II Round II Number 4 If n is the largest integer so that 6 n divides 10!, what is n?

16 Division II Round II Number 5 If is expressed as a rational number in reduced form, then the value of the numerator is what?

17 Division II Round II Number 6 Mark has a cylindrical storage unit with radius 2 ft and height of 3 ft. He has two spherical basketballs that he stores there both with 6 inch radii. If the volume that remains in the storage is kπ 3, what is k?

18 Division II Round II Number 7 A ball is dropped vertically from a height of 16 feet and each time it bounces it rebounds back vertically one-half the height it had previously fallen. What is the total distance the ball travels?

19 Division II Round III Ciphering Participants in Round III ciphering from Division II schools should now make their way to the front.

20 Division II Round III Number 1 Five houses in a row are each to be painted with the colors red, blue, and green. In how many different ways can the houses be painted so that no two adjacent houses are of the same color?

21 Division II Round III Number 2 In the figure below, AB BC, BC CD, AB = 8, BC = 5, and CD = 4. What is the shortest distance from A to D? C D A B

22 Division II Round III Number 3 What is the unit s digit of the number ?

23 Division II Round III Number 4 The line L with equation 3x + y = 12 passes through the point (3, 3). What is the y-intercept of the line perpendicular to L also passing through the point (3, 3)?

24 Division II Round III Number 5 If log 10 x 3 = log What is x?

25 Division II Round III Number 6 A movie theater sold tickets for three hundred seats and the box office receipts of $2400 came from $9 adult tickets and $6 child tickets. How many more adult tickets than children tickets were sold?

26 Division II Round III Number 7 How many diagonals does a hexagon have?

27 Division I Round I Ciphering Participants in Round I ciphering from Division I schools should now make their way to the front.

28 House Rules 1. All answers are integers(!) 2. All answers must be written in standard form. For example, 8 not 2 3, and 10, not ( 5 2).

29 Division I Round I Number 1 If you were to roll a die until you rolled a six, the chance you would stop after the third roll is k 216. What is k?

30 Division I Round I Number 2 How many ways are there to spell FURMANU in the following diagram? Your movement in the diagram is restricted to always be southeast or southwest beginning at F. F U U R R R M M M M A A A N N U

31 Division I Round I Number 3 Last week we added a new bag of 100 M&M s to our existing stash. Each day of that week our department s stash of M&M s diminished by 40%. At the end of the third day, 54 M&M s were left. How many were in the jar at the beginning of the week before we added more?

32 Division I Round I Number 4 A Furman student dropped by the bookstore to buy a pencil before class. The bill is $0.73, and she gives the cashier $1.00. The cashier has available 1 quarter, 2 dimes, 3 nickels, and 2 pennies. In how many ways can the cashier make change?

33 Division I Round I Number 5 If (a 1,a 2 ) is the center and r is the radius of the circle with equation what is 64( a 1+a 2 r ) 3? (x + 3) 2 + y 2 3y = 7 4,

34 Division I Round I Number 6 What is the radius of the circle whose general equation is given by 4x 2 + 4y x 16y + 37 = 0?

35 Division I Round I Number 7 What is 8 8 8?

36 Division I Round II Ciphering Participants in Round II ciphering from Division I schools should now make their way to the front.

37 Division I Round II Number students took a 3-question math exam. 114 students answered the first question correctly, 50 the second, and 41 the third. Moreover, 14 answered the first two correctly, 15 answered the second and the third correctly and 11 the first and third. 5 answered all three correctly. How many students answered no question correctly?

38 Division I Round II Number 2 Evaluate 27(log log ).

39 Division I Round II Number 3 If x, y are in [0, π 2 ] and sin(x) = 3 5 and sec(y) = 5 4, evaluate 25 sin(x + y).

40 Division I Round II Number 4 A trapezoid has two parallel sides of length b 1 and b 2. It has a height of 3 and an area of 18. If one of the sides, b 1 or b 2, is twice the length of the other, what is the length of the larger of b 1 and b 2?

41 Division I Round II Number 5 Two angles are supplementary and one, x, is 20 o more than three times the other, y. Find x y.

42 Division I Round II Number 6 If g(x) = 2x x+3 and f(g(x)) = x, then what is 3f( 2)?

43 Division I Round II Number 7 If the operation is defined by the equation x y = 2x + y, what is the value of a in the equation 2 a = a 3?

44 Division I Round III Ciphering Participants in Round III ciphering from Division I schools should now make their way to the front.

45 Division I Round III Number 1 When x = 1 and y = 1, what is the value of 2 4 x x 3 y x 2 y xy 3 + y 4?

46 Division I Round III Number 2 Evaluate log

47 Division I Round III Number 3 The vertices of triangle ABC are (4, 3), (4, 7), and (8, 3). What is the sum of the area of ABC and (2 2) times the perimeter of ABC?

48 Division I Round III Number 4 A company is considering hiring some employees. Currently it takes 10 employees, working 8 hours a day, all at the same rate, to produce 400 widgets. If two people are hired, and they work at the same rate as the current employees, how many more widgets can the company produce per eight hour day?

49 Division I Round III Number 5 There are 200 questions on a 3-hour examination. Among these questions are 50 mathematics problems. It is suggested that twice as much time be allowed for each mathematics problem as for each of the other questions. How many minutes should be spent on the mathematics problems combined?

50 Division I Round III Number 6 Two triangles are similar. The sides of one are 9, 12, 15. If the perimeter of the second triangle is 24, find the product of the sides of the second triangle.

51 Division I Round III Number 7 Consider the following sequence of terms: {0, 1 3, 3 6, 7 11, 15 18,A,B,C, } What is the sum of the numerator and denominator in the term C?

52 That s All, Folks Awards Ceremony to follow soon. Please be patient while we tally the results.

Furman University Wylie Mathematics Tournament Ciphering Competition. March 11, 2006

Furman University Wylie Mathematics Tournament Ciphering Competition March 11, 2006 House Rules 1. All answers are integers(!) 2. All answers must be written in standard form. For example, 8 not 2 3, and