Transcript First Annual Holy Cross High School Mathematics Competition

First Annual Holy Cross High School
Mathematics Competition
Individual Competition
1. Each of 2005 fractions has an even numerator and
an odd denominator. If the product of all of them is an
integer, it must be
A. Even
B. Odd
C. Prime
D. 2005
2. If x is a whole number, what is the largest possible
perimeter of a triangle with sides 3, 4, and x?
A. 11
B. 12
C. 13
D. 14
3. I phoned my Mom to help me answer this, the final
question on a quiz show: “How many integers equal their
own squares?” Mom said, “_____.” She was right!
A. zero
B. one
C. two
D. three
4. A square has a perimeter of 4. What is the area?
A. 1
B. 4
C. 8
D. 16
5.
A. 1
1
1
1
2  4  6 
2
4
6
B. 6
C. 12
D. 24
6. When I add the measures of any two angles of triangle T,
the sum is always 120°. Triangle T must be
A. Scalene
B. Right
C. Obtuse
D. Equiangular
7. 30%  40% 
A. 12%
B. 120%
C. 1200%
D. 12,000%
8. If
2
of a cup of fish food can feed 8 goldfish, then
3
4 cups of fish food should be able to feed ______ goldfish?
A. 12
B. 24
C. 36
D. 48
9. If 4x 
1
A.
8
the reciprocal of
1
B.
2
1
, then x could equal
3
x
C. 2
D. 8
10. Suppose I have $2.00 in nickels, dimes, and quarters.
If I have the same number of each type of coin, how many
coins do I have?
A. 6
B. 9
C. 12
D. 15
11. The cheapest way to move is by mail, so each time
I move, I mail myself to my new home. I’ve done this as
many times as the number of different integers that
satisfy
2
2
2
n

1
n

2
n
 
  3  0 .
How many times did I move by mail?
A. 1
B. 2
C. 3
D. 6
12.
x400 ÷ x100 =
A. x500
B. x300
C. x4
D. 4
13. Circle C’s center is (0, 0) and the length of
C’s radius is 5. Which of the following are the
coordinates of a point on C?
A. (0, 5)
B. (-5, -5)
C. (-10, 0)
D. (5, 5)
14. Find the sum of all the common factors of 32 and 64.
A. 63
B. 62
C. 31
D. 30
15. A square piece of paper is folded in half vertically.
If the resulting figure has a perimeter of 18 cm, what is
the area of the original square?
A. 81 cm2
B. 18 cm2
C. 24 cm2
D. 36cm2
16. 7 is a prime number, so May 7th is a prime day. In all,
May has _____ prime days?
A. 10
B. 11
C. 12
D. 13
17. The difference between
1
A.
5
B.
1
6
6
and its reciprocal is
5
1
C.
30
11
D.
30
18. If the sum of the squares of two numbers is equal to
the square of their sum, then the product of these two
numbers must be
A. 0
B. 1
C. 4
D. 16
19. For which of the following is nn the square of
an integer?
A. n = 3
B. n = 5
C. n = 6
D. n = 7
20. Joni travels 14 blocks east, then 3 blocks south,
then 19 blocks west, and then 3 blocks north. How many
blocks is she from where she started?
A. 27
B. 11
C. 8
D. 5
21. A bag contains a total of 14 balls: 4 red balls, 3 blue
balls, and 7 white balls. Two balls are drawn at random
without replacement. What is the probability that both
balls are red?
A. 6
91
B. 9
182
C. 6
92
12
D.
92
22. In the figure below, both circles have the same center.
The radius of the larger circle is R. The radius of the
smaller circle is 3 less than R. Which of the following
represents the area of the non-shaded region?
A.  R 2
C.   3
B.   R2   R  32 


2
D.   R  3
2
3
23. On a map,
inch represents 72 miles. How many
8
miles does 1 2 inches represent?
3
A. 360
B. 320
C. 192
D. 120
24. How many different rectangles of all sizes are in the
figure below?
A. 30
B. 20
C. 18
D. 10
25. Consider the operation # such that a # b = -3a + b2.
Find (-2 # 3) # 6.
A. -9
B. 9
C. 15
D. 27