SW-ARML 10-24-10 Problem 1. A function is given by the table f(x) 1 2 3 4 5 6 x 4 2 6 3 1 5 f(x) If is a sequence given by = 4 and = for all a1 ak+1 f(ak) k a2010. ≥ 1, find Let and all be positive numbers, and let be a such that . Find . Problem 2. x, y, z w Problem 3. Find the product of the real roots of the equation . Problem The number 1557, 1227, and 1341 have something in common. Each is a four-digit 4. number beginning with 1 that has exactly two identical digits. How many such four-digit numbers are there? Problem 5. Let and . Find the integer closest to . a – b Problem 6. How many zeros does the number end? Problem 7. Find the minimum value of for 0 < < . x Problem 8. What is the largest 2-digit prime factor of the integer ? Problem 9. Let is a sequence given by all Find the remainder upon dividing by n ≥ 1. a2010 49. Problem 10. Let be the smallest positive integer that is a multiple of 75 and has exactly 75 n positive integer divisors, including 1 and itself. Find .
SW-ARML 10-24-10 Problem 1. A function f(x) is given by the table x 1 2 3 4 5 6 f(x) 4 2 6 3 1 5 If is a sequence given by a1 = 4 and ak+1 = f(ak) for all k ≥ 1, find a2010. Problem 2. Let x, y, and z all be positive numbers, and let w be a such that . Find . Problem 3. Find the product of the real roots of the equation . Problem 4. The number 1557, 1227, and 1341 have something in common. Each is a four-digit number beginning with 1 that has exactly two identical digits. How many such four-digit numbers are there? Problem 5. Let and . Find the integer closest to a – b . Problem 6. How many zeros does the number end? Problem 7. Find the minimum value of for 0 < x < . Problem 8. What is the largest 2-digit prime factor of the integer ? Problem 9. Let is a sequence given by all n ≥ 1. Find the remainder upon dividing a2010 by 49. Problem 10. Let n be the smallest positive integer that is a multiple of 75 and has exactly 75 positive integer divisors, including 1 and itself. Find .
Practice_10-24-10.docx