Download Test - FloridaMAO

2005 FAMAT State Convention
Interschool Test
Directions: Write all answers on the answer sheet provided. Leave all
answers exact and simplified unless otherwise specified.

1. For positive integers a and b, a b
 x  b
a . Express x in terms of a and b.
2. Find the two terms which continue the pattern: 1, 2, 6, 20, 70, 252, ___, ___
3. Who are Shake Zulu, Frylock, and Meatwad collectively known as?
4. The number 2005 is a multiple of 5 whose digits add to 7.
Let A = the smallest integer greater than 2005 which is a multiple of 5 and
whose digits add to 7
Let B = the smallest integer greater than 2005 which is a multiple of 7 and
whose digits add to 5
Find the product of A and B.
5. What game show regularly featured a Flokati rug as one of its first-round prizes?
6. What is the only positive integer which can be represented simultaneously by
a 2  a 3  a 4  a 5  a 6 and by a 7  a 2 for some integer a ?
7. Neo gives you 6 red pills, 6 blue pills, and 2 bowls. You are to distribute all 12 pills
into the 2 bowls however you wish, but you may not break the pills into pieces.
Once you arrange the pills, Neo (now blindfolded) will randomly select one bowl,
then one pill from that bowl. You can distribute the pills in a way to maximize the
probability that Neo chooses a red pill. What is the maximum probability that Neo
takes a red pill?
8. On the TV show Friends, what is Chandler Bing’s middle name?
9. Georges Vantongerloo constructed a 1935 piece whose title consists of 2 binomials
in terms of x. What is the product of these binomials times the year of
Vantongerloo’s death?
10. Consider the 1st digit of  to be 3, the 2nd digit 1, the 3rd digit 4, and so on. If
A = the 31st digit
B = the 314th digit
C = the 3141st digit
D = the 999988th digit
Find the value of AB C D .
11. Using each of the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 exactly once, fill in the boxes to
make the equation true:


5
12. Complete the following “magic square”:
Maggie Smith
Tatum O’Neal
Ingrid Bergman
Cloris Leachman
Lee Grant
Vanessa Redgrave
13. Nine different positive integers appear in the word search below. When these 9
numbers are placed in numerical order, beginning with the smallest, they form a 9term sequence. What number would be the 10th term to continue the sequence?
R
I
X
E
T
H
R
E
E
S
O
U
N
V
E
L
E
V
E
E
N
F
O
U
I
V
I
V
I
N
I
E
N
F
T
F
E
G
T
O
N
T
E
R
Y
W
H
S
R
Y
I
E
W
T
O
T
E
W
O
T
S
H
F
E
R
V
R
L
F
N
O
I
O
E
E
I
F
I
V
E
F
S
U
R
Z
L
H
E
H
W
O
Y
T
F
I
O
W
T
E
T
14. What is the smallest whole number which cannot be the score of any cribbage
hand?
15. Fill in the boxes with 5 cards which will score 18 points in one cribbage hand.
cards in hand
upcard
16. The sequence of numbers 145, 150, 156, 180, 219, 240, 306, 340, 444, 585, 656,
870, 1300, 1731, 2594, and _______ has something to do with the number 144.
What number fills in the blank?
17. Match each mathematician with the mathematical symbol that each introduced.
On the answer sheet, write the symbol next to the correct name.
Thomas Harriot
Christian Kramp
William Oughtred
Robert Recorde
Christoff Rudolff
John Wallis
Johann Widman



!

18. So, how much did Ken Jennings actually win on his 75 regular-season Jeopardy!
shows? Please give the amount that he won before taxes.
19. If Jen Jennings, Ken’s evil twin, won the absolute maximum amount of money in a
given regular-season Jeopardy! game, how many complete games winning this
maximum amount would it take her to surpass Ken’s grand total?
20. Four of each of the numbers 2, 3, 4, and 6 should be placed in the outlined boxes
in the puzzle to make valid equations across and down. There should only be one
of each number in each row and column. Standard order of operations does not
apply to this puzzle – all equations are read and simplified from left to right or
from top to bottom.
X
-
X
+
X
X
-
+
=
20
X
X
+
=
4
X
+
=
12
26
+
=
X
11
+
=
+

+
=
15
X
-
=
-

X
+
+
4
+
=
10
+
=
51
21. The radius of a sphere is R. By how much should you increase the value of R if
you wish to increase the volume of the sphere by 50%?
22. Using the sphere from question 21, by how much should you decrease the value of
R if you wish to decrease the sphere’s surface area by 25%?
23. Throughout the entire series of The Bob Newhart Show, how many times was the
phrase “Hi, Bob” uttered?
24. The ellipse 64 x 2  100 y 2  640 x  800 y  3200  0 is revolved about its major axis,
creating a solid with volume V. If the ellipse is revolved about its minor axis, a
solid with volume W is created. What is the value of V  W ?
25. If A =
 1  x2 
1 1 1 1 1 1
0  x4  1 dx and B = 1  3  5  7  9  11  13  ... , find the value of AB.
1
26. An Indian chief had 3 wives who were preparing to give birth. One wife was to
give birth on a bear hide, the second wife on a buffalo hide, and the third on a
hippopotamus hide. The first wife bore the chief a daughter, the second wife had
a son, and the third wife gave birth to twins, one boy and one girl. This proves
that ___________________________________________.
27. In the chart below, draw a path moving up, down, left, or right, but not diagonally,
to connect each pair of matching letters. Each path must begin in the center of a
square and pass through the center of each square it passes through. Also, no
path may cross over itself or any other path, and each square must be passed
through exactly once.
A B
B
C
A D E
C
F
E
D
F
28. When .13  .2 4  .35  .4 6  ...  .810 is evaluated in base 10, it can be written as a
A
fraction , which is in lowest terms. What is the base 10 sum of A and B?
B
29. How many complex values of x satisfy the equation
1 2 3 4
n
 3  5  7  ...  2 n 1  ...  1 ?
x x
x
x
x
30. What are the real values of x which satisfy the equation in the previous question?
You may round these to 3 decimal places each.
31. What is the probability of throwing a zilch on your first roll in the dice game Zilch?
32. AzzOzzIzz zO zzE zUzzEzz zzzzE, zOz zAzz zzAzzzIzzz zEzE zAzEz Iz zzE zIE? Your
answer should be a positive integer.
33. YGJXCKVHKUUGVOYKQVRGNGWTUJV? Again, the answer to this question is a
positive integer.
34. For this question, use the current FAMAT individual test scoring system. If a
student answers all 30 questions on an individual test and has X answers correct,
his FAMAT score will be the same as his percent score. What is X?
35. According to the third edition of the Official Scrabble Player’s Dictionary, there are
96 two-letter words. Some of these words are also numbers represented in
Roman numerals. What is the sum of all of these Roman numeral “words”? Write
your answer as a Roman numeral.
36. What are the 3 cities which continue the pattern:
Carson City, Tallahassee, Atlanta, Harrisburg, Richmond, _____, _____, _____?
37. Match each clue to the Florida county to which it refers.
Charlotte
Citrus
Hernando
Jackson
Jefferson
Marion
Pinellas
Santa Rosa
Walton
A.
B.
C.
D.
E.
F.
G.
H.
I.
Most densely populated
Contains state’s geographic center
County courthouse styled after Monticello
Punta Gorda located here
Two Egg located here
Crystal River State Archaeological Site located here
Leads Florida in petroleum production
Contains highest point of elevation in state
Part of Bond movie Moonraker filmed here
38. Given ABC with vertices A(0, 3); B(12, 6); C(9, 15); circumcenter D,
orthocenter E, and centroid F. What is the length of the altitude to the
shortest side of DEF ?
39. If a#b = 2a+3b and a&b = 5ab + b#a, what is the value of 7#8 – 7&8?
40. 



41. What is the smallest natural number with a persistence of 11?
42. What are the next 3 numbers which complete the pattern
1
1 1 2
0, 1, , 2, 3, 1, , , , _____, _____, _____?
2
3 4 3
43. Using only the letters A, B, C, …, J once each, place one letter in each box to
create a 3-letter word and a 5-letter word going across, and a 3-letter word going
down. One letter will not be used.



44. What was the first college football team to win 700 games?
45. What 6-letter French word for a bird contains all of the vowels?
46. In the figure below, V is the center of a semicircle of radius 4. WX = XY = 2.
If UX + UY = P  Q , for integers P and Q, find the value of P + Q.
47. The natural numbers from 1 to 12 inclusive are placed at random in the chart
below so that each box contains one unique number. What is the probability that
the first 4 numbers are in increasing order?
48. Who is this design named for?
49. In RST , mS  135 , RS = 2, and ST = 3. What is the length of altitude SH ?
50. In the figure below, a circle with radius 1 is placed inside an equilateral triangle
with side length 12. The circle and triangle are both in the same plane. The circle
may move around freely inside the triangle, but it must stay completely in the
interior of the triangle. A point P is selected at random inside the triangle. What is
the probability that the circle can be moved so that the center of the circle
coincides with P?
51. Choose any one number from the set {1, 2, 3, 4, …, 99, 100} and write it on your
answer sheet. Credit will be awarded only to the school which writes the smallest
unique answer and to the school which writes the largest unique answer.