#### 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 32 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