2015 AMC 12A Problems2015 AMC 12A Problems.docVIP

2015 AMC 12A Problems Problem 1 What is the value of Problem 2 Two of the three sides of a triangle are 20 and 15. Which of the following numbers is not a possible perimeter of the triangle? Problem 3 Mr. Patrick teaches math to 15 students. He was grading tests and found that when he graded everyones test except Paytons, the average grade for the class was 80. after he graded Paytons test, the class average became 81. What was Paytons score on the test? Problem 4 The sum of two positive numbers is 5 times their difference. What is the ratio of the larger number to the smaller? Problem 5 Amelia needs to estimate the quantity , where and are large positive integers. She rounds each of the integers so that the calculation will be easier to do mentally. In which of these situations will her answer necessarily be greater than the exact value of ? Problem 6 Two years ago Pete was three times as old as his cousin Claire. Two years before that, Pete was four times as old as Claire. In how many years will the ratio of their ages be ? Problem 7 Two right circular cylinders have the same volume. The radius of the second cylinder is more than the radius of the first. What is the relationship between the heights of the two cylinders? Problem 8 The ratio of the length to the width of a rectangle is ?: . If the rectangle has diagonal of length , then the area may be expressed as for some constant . What is ? Problem 9 A box contains 2 red marbles, 2 green marbles, and 2 yellow marbles. Carol takes 2 marbles from the box at random; then Claudia takes 2 of the remaining marbles at random; and then Cheryl takes the last 2 marbles. What is the probability that Cheryl gets 2 marbles of the same color? Problem 10 Integers and with satisfy . What is ? Problem 11 On a sheet of paper, Isabella draws a circle of radius , a circle of radius , and all possible lines simultaneously tangent to both circles. Isabella notices that she has drawn exactly lines. How m