2015 AMC 8 Problems
Contents
[hide]Problem 1
How many square yards of carpet are required to cover a rectangular floor that is feet long and feet wide? (There are 3 feet in a yard.)
Problem 2
Point is the center of the regular octagon , and is the midpoint of the side What fraction of the area of the octagon is shaded?
[asy] pair A,B,C,D,E,F,G,H,O,X; A=dir(45); B=dir(90); C=dir(135); D=dir(180); E=dir(-135); F=dir(-90); G=dir(-45); H=dir(0); O=(0,0); X=midpoint(A--B);
fill(X--B--C--D--E--O--cycle,rgb(0.75,0.75,0.75)); draw(A--B--C--D--E--F--G--H--cycle);
dot("",A,dir(45)); dot("",B,dir(90)); dot("",C,dir(135)); dot("",D,dir(180)); dot("",E,dir(-135)); dot("",F,dir(-90)); dot("",G,dir(-45)); dot("",H,dir(0)); dot("",X,dir(135/2)); dot("",O,dir(0)); draw(E--O--X); [/asy]
Problem 3
Jack and Jill are going swimming at a pool that is one mile from their house. They leave home simultaneously. Jill rides her bicycle to the pool at a constant speed of miles per hour. Jack walks to the pool at a constant speed of miles per hour. How many minutes before Jack does Jill arrive?
Problem 4
The Centerville Middle School chess team consists of two boys and three girls. A photographer wants to take a picture of the team to appear in the local newspaper. She decides to have them sit in a row with a boy at each end and the three girls in the middle. How many such arrangements are possible?
Problem 5
Billy's basketball team scored the following points over the course of the first 11 games of the season: If his team scores 40 in the 12th game, which of the following statistics will show an increase?
Problem 6
In , , and . What is the area of ?
Problem 7
Each of two boxes contains three chips numbered , , . A chip is drawn randomly from each box and the numbers on the two chips are multiplied. What is the probability that their product is even?
Problem 8
What is the smallest whole number larger than the perimeter of any triangle with a side of length and a side of length ?
Problem 9
On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had Janabel sold after working days?