Download File - San Diego Math Field Day

Math Field Day 2009
Tri-Team Attack Part I
1.
Write the year 2009 In Roman Numerals.
2.
If the side lengths of a triangle are 6, 2x – 1, and x + 4, then what is the
positive difference between the greatest and least integral values that x
can be?
3.
Juan's street has four-digit house numbers. He notices that the sum of the
four digits of his house total 30. What is the maximum number of houses
that can have this quality?
4.
An analog clock reads 10:20 am. What is the measure, in degrees, of the
smallest angle that is formed between the hour and minute hands?
5.
A regular hexagon has an area of 24 3 . What is the length of its longest
diagonal?
6.
What is the sum of the series 50 – 49 + 48 – 47 + . . . + 4 – 3 + 2 - 1?
7.
How many positive factors does the number 33,075 have?
8.
In mathematics, a semi-prime number is a whole number that is the
product of exactly two prime numbers (they can be the same number).
What is the tenth semi-prime number?
9.
A right triangle has one of its sides be 15 ft. If all of its side lengths are
whole numbers, then what is the least possible number of feet in its
perimeter?
10.
The sum of two numbers is 24. When each is squared, the difference is
144. What is the positive difference of the two numbers?
11.
How many segments can be drawn using 9 points if no more than any two
of the points are collinear?
12.
A square is inscribed in a circle of radius 10 cm. What is the positive
difference between the area of the circle and the square? Round your
answer to the nearest tenth of a square centimeter.
13.
What is the only three-digit positive integer that has exactly five distinct,
positive factors?
14.
How many ways can you rearrange the letters of the word TANGENT?
15.
1 1 2
 
. If a  b and both a and b are positive whole numbers, find
a b 15
the smallest value of a  b .
16.
In Exactburgh, they have only two denominations of money, $5 and $8
bills. Also, everyone always pays exactly the amount that something is
priced. What is the largest integer dollar amount that an item CANNOT
be priced in Exactburgh?
17.
The square of a number is also a factor of 6!. What is the greatest possible
value of the original number?
18.
Zoey wants to cut up a block of cheese into 12 pieces. What is the fewest
number of slices she needs to make?
19.
What is the 75th positive composite number?
20.
Three years ago Frances was a third the age of his brother Bill. Four years
from now, he will be half of Bill's age. How many years old is Bill now?
Math Field Day 2009
Tri-Team Attack Part I
Answer Key
1.
MMIX
2.
8
3.
84
4.
170
5.
8
6.
25
7.
36
8.
26
9.
36
10.
6
11.
36
12.
114.2
13.
625
14.
2,520
15.
32
16.
27
17.
12
18.
4
19.
102
20.
24