2016年度AMC12B试题及解答.docx

,. ,. 2016 AMC 12B Problem 1 What is the value of when ? Solution By: Dragonfly We find that is the same as , since a number to the power of is just the reciprocal of that number. We then get the equation to be We can then simplify the equation to get Problem 2 The harmonic mean of two numbers can be calculated as twice their product divided by their sum. The harmonic mean of and to which integer? is closest Solution By: dragonfly Since the harmonic mean is times their product divided by their sum, we get the equation which is then which is finally closest to . Problem 3 Let . What is the value of ? Solution By: dragonfly First of all, lets plug in all of the 's into the equation. Then we simplify to get which simplifies into and finally we get Problem 4 The ratio of the measures of two acute angles is , and the complement of one of these two angles is twice as large as the complement of the other. What is the sum of the degree measures of the two angles? Solution By: dragonfly We set up equations to find each angle. The larger angle will be represented as and the larger angle will we represented as , in degrees. This implies that and since the larger the original angle, the smaller the complement. We then find that and , and their sum is Problem 5 The War of started with a declaration of war on Thursday, June , . The peace treaty to end the war was signed days later, on December , . On what day of the week was the treaty signed? Solution By: dragonfly To find what day of the week it is in days, we have to divide by to see the remainder, and then add the remainder to the current day. We get that has a remainder of 2, so we increase the current day by to get Problem 6 All three vertices of with at the origin and is . What is the length of lie on the parabola defined by , parallel to the -axis. The area of the triangle ? Solution By: Albert471 Plotting points and on the graph shows that they are at and , which is isosceles. By setting up the triangle area formul