AMC10美国数学超详细竞赛真题2002A卷.docx

Problem 1The ratiois closest to which of the following numbers?SolutionProblem 2Given that a, b, and c are non-zero real numbers, define.Find.Solution Problem 1 The ratio is closest to which of the following numbers? Solution Problem 2 Given that a, b, and c are non-zero real numbers, define . Find . Solution Problem 3 According to the standard convention for exponentiation, . If the order in which the exponentiations are performed is changed, how many other values are possible? Solution Problem 4 For how many positive integers ? is there at least 1 positive integer such that infinitely many Solution Problem 5 Each of the small circles in the figure has radius one. The innermost circle is tangent to the six circles that surround it, and each of those circles is tangent to the large circle and to its small-circle neighbors. Find the area of the shadedregion.SolutionProblem 6From a starting number, Cindy was supposed to subtract 3, and then divide by 9,but instead, Cindy subtracted 9, then divided by 3, getting 43. If the correct instructions were followed, what would the result be? the large circle and to its small-circle neighbors. Find the area of the shaded region. Solution Problem 6 From a starting number, Cindy was supposed to subtract 3, and then divide by 9, but instead, Cindy subtracted 9, then divided by 3, getting 43. If the correct instructions were followed, what would the result be? Solution Problem 7 A arc of circle A is equal in length to a arc of circle B. What is the ratio of circle A's area and circle B's area? Solution Problem 8 Betsy designed a flag using blue triangles, small white squares, and a red center square, as shown. Let of the white squares, and correct? be the total area of the blue triangles, the total area the area of the red square. Which of the following is Solution Problem 9There are 3 numbers A, B, and C, such that. What is the average of A, B, and C?, andNot uniquely Problem 9 There are 3 numbers A, B, and C, such that . What is