First Annual Holy Cross High School

Mathematics Competition

Individual Competition

1. Each of 2005 fractions has an even numerator andan 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. 1 1 1

2 4 62 4 6

A. 1 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 of a cup of fish food can feed 8 goldfish, then

4 cups of fish food should be able to feed ______ goldfish?

A. 12 B. 24 C. 36 D. 48

2

3

9. If the reciprocal of , then x could equal

A. B. C. 2 D. 8

4x 3

1

x

1

8

1

2

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 .

How many times did I move by mail?

A. 1 B. 2 C. 3 D. 6

2 2 21 2 3 0n n n

12. x400 ÷ x100 =

A. x500 B. x300 C. x4 D. 4

13. Circle C’s center is (0, 0) and the length ofC’s radius is 5. Which of the following are thecoordinates 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 and its reciprocal is

A. B. C. D.

6

5

1

5

1

61

30

11

30

18. If the sum of the squares of two numbers is equal tothe square of their sum, then the product of these twonumbers must be

A. 0 B. 1 C. 4 D. 16

19. For which of the following is nn the square ofan 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 manyblocks 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 blueballs, and 7 white balls. Two balls are drawn at randomwithout replacement. What is the probability that bothballs are red?

A. B. C. D.6

91

9

182

6

92

12

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. B.

C. D.

2R 22 3R R

23 23R

23. On a map, inch represents 72 miles. How many

miles does inches represent?

A. 360 B. 320 C. 192 D. 120

3

8213

24. How many different rectangles of all sizes are in thefigure 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