2015 AMC 8 真题与答案及免费中文视频详解(翰林独家)

2015 AMC 8 Problems & Solutions

2015AMC 8 真题与答案及中文视频详解(翰林独家)

Problem 1

How many square yards of carpet are required to cover a rectangular floor that is  feet long and  feet wide? (There are  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?

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 Dragonvale 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  games of the season:If his team scores 40 in the 12th game, which of the following statistics will show an increase?

Problem 11

In the small country of Icosahedrontopia, all automobile license plates have four symbols. The first must be a vowel ( or ), the second and third must be two different letters among the  non-vowels, and the fourth must be a digit ( through ). If the symbols are chosen at random subject to these conditions, what is the probability that the plate will read ""?

Problem 12

How many pairs of parallel edges, such as  and  or  and , does a cube have?

Problem 13

How many subsets of two elements can be removed from the set  so that the mean (average) of the remaining numbers is ?

Problem 14

Which of the following integers cannot be written as the sum of four consecutive odd integers?

Problem 15

At Euler Middle School,  students voted on two issues in a school referendum with the following results:  voted in favor of the first issue and  voted in favor of the second issue. If there were exactly  students who voted against both issues, how many students voted in favor of both issues?

Problem 16

In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If  of all the ninth graders are paired with  of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy?

Problem 17

Jeremy's father drives him to school in rush hour traffic in  minutes. One day there is no traffic, so his father can drive him  miles per hour faster and gets him to school in  minutes. How far in miles is it to school?

Problem 18

An arithmetic sequence is a sequence in which each term after the first is obtained by adding a constant to the previous term. For example,  is an arithmetic sequence with five terms, in which the first term is  and the constant added is . Each row and each column in this  array is an arithmetic sequence with five terms. What is the value of ?

Problem 19

A triangle with vertices as , , and  is plotted on a  grid. What fraction of the grid is covered by the triangle?

Problem 20

Ralph went to the store and bought  pairs of socks for a total of . Some of the socks he bought cost  a pair, some of the socks he bought cost  a pair, and some of the socks he bought cost  a pair. If he bought at least one pair of each type, how many pairs of  socks did Ralph buy?

Problem 21

In the given figure hexagon  is equiangular,  and  are squares with areas  and  respectively,  is equilateral and . What is the area of ?

Problem 22

On June , a group of students are standing in rows, with  students in each row. On June , the same group is standing with all of the students in one long row. On June , the same group is standing with just one student in each row. On June , the same group is standing with  students in each row. This process continues through June  with a different number of students per row each day. However, on June , they cannot find a new way of organizing the students. What is the smallest possible number of students in the group?

Problem 23

Tom has twelve slips of paper which he wants to put into five cups labeled , , , , . He wants the sum of the numbers on the slips in each cup to be an integer. Furthermore, he wants the five integers to be consecutive and increasing from  to . The numbers on the papers are  and . If a slip with  goes into cup  and a slip with  goes into cup , then the slip with  must go into what cup?

Problem 24

A baseball league consists of two four-team divisions. Each team plays every other team in its division  games. Each team plays every team in the other division  games with  and . Each team plays a -game schedule. How many games does a team play within its own division?

Problem 25

One-inch squares are cut from the corners of this  inch square. What is the area in square inches of the largest square that can fit into the remaining space?

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