2015 AMC 12A Problems Problem 1 What is the value of Problem 2 Two of the three sides ofa 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 everyone's test except Payton's, the average grade for the class was 80. after he graded Payton's test, the class average became 81. What was Payton's score on the test? Problem 4 The sum of two positive numbers is5 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 ofa rectangle is:. If the rectangle has diagonal of length , then the area may be expressed as for some constan
