2015 AMC 8 真题与答案解析

2015 AMC 8 真题

答案解析请参考文末

Problem 1

How many square yards of carpet are required to cover a rectangular floor that is 2015 AMC 8 Problems feet long and 2015 AMC 8 Problems feet wide? (There are 2015 AMC 8 Problems feet in a yard.)

2015 AMC 8 Problems

 

Problem 2

Point 2015 AMC 8 Problems is the center of the regular octagon 2015 AMC 8 Problems, and 2015 AMC 8 Problems is the midpoint of the side 2015 AMC 8 Problems What fraction of the area of the octagon is shaded?

2015 AMC 8 Problems

2015 AMC 8 Problems

 

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 2015 AMC 8 Problems miles per hour. Jack walks to the pool at a constant speed of 2015 AMC 8 Problems miles per hour. How many minutes before Jack does Jill arrive?

2015 AMC 8 Problems

 

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?

2015 AMC 8 Problems

 

Problem 5

Billy's basketball team scored the following points over the course of the first 2015 AMC 8 Problems games of the season: 2015 AMC 8 Problems If his team scores 40 in the 12th game, which of the following statistics will show an increase?

2015 AMC 8 Problems

 

Problem 6

In 2015 AMC 8 Problems, 2015 AMC 8 Problems, and 2015 AMC 8 Problems. What is the area of 2015 AMC 8 Problems?

2015 AMC 8 Problems

 

Problem 7

Each of two boxes contains three chips numbered 2015 AMC 8 Problems, 2015 AMC 8 Problems, 2015 AMC 8 Problems. 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?

2015 AMC 8 Problems

 

Problem 8

What is the smallest whole number larger than the perimeter of any triangle with a side of length 2015 AMC 8 Problems and a side of length 2015 AMC 8 Problems?

2015 AMC 8 Problems

 

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 2015 AMC 8 Problems days?

2015 AMC 8 Problems

 

Problem 10

How many integers between 2015 AMC 8 Problems and 2015 AMC 8 Problems have four distinct digits?

2015 AMC 8 Problems

 

Problem 11

In the small country of Mathland, all automobile license plates have four symbols. The first must be a vowel (2015 AMC 8 Problems or 2015 AMC 8 Problems), the second and third must be two different letters among the 2015 AMC 8 Problems non-vowels, and the fourth must be a digit (2015 AMC 8 Problems through 2015 AMC 8 Problems). If the symbols are chosen at random subject to these conditions, what is the probability that the plate will read "2015 AMC 8 Problems"?

2015 AMC 8 Problems

 

Problem 12

How many pairs of parallel edges, such as 2015 AMC 8 Problems and 2015 AMC 8 Problems or 2015 AMC 8 Problems and 2015 AMC 8 Problems, does a cube have?

2015 AMC 8 Problems

2015 AMC 8 Problems

 

Problem 13

How many subsets of two elements can be removed from the set 2015 AMC 8 Problems so that the mean (average) of the remaining numbers is 2015 AMC 8 Problems?

2015 AMC 8 Problems

 

Problem 14

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

2015 AMC 8 Problems

 

Problem 15

At Euler Middle School, 2015 AMC 8 Problems students voted on two issues in a school referendum with the following results: 2015 AMC 8 Problems voted in favor of the first issue and 2015 AMC 8 Problems voted in favor of the second issue. If there were exactly 2015 AMC 8 Problems students who voted against both issues, how many students voted in favor of both issues?

2015 AMC 8 Problems

 

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 2015 AMC 8 Problems of all the ninth graders are paired with 2015 AMC 8 Problems of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy?

2015 AMC 8 Problems

 

Problem 17

Jeremy's father drives him to school in rush hour traffic in 2015 AMC 8 Problems minutes. One day there is no traffic, so his father can drive him 2015 AMC 8 Problems miles per hour faster and gets him to school in 2015 AMC 8 Problems minutes. How far in miles is it to school?

2015 AMC 8 Problems

 

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, 2015 AMC 8 Problems is an arithmetic sequence with five terms, in which the first term is 2015 AMC 8 Problems and the constant added is 2015 AMC 8 Problems. Each row and each column in this 2015 AMC 8 Problems array is an arithmetic sequence with five terms. What is the value of 2015 AMC 8 Problems?

2015 AMC 8 Problems

2015 AMC 8 Problems

 

Problem 19

A triangle with vertices as 2015 AMC 8 Problems, 2015 AMC 8 Problems, and 2015 AMC 8 Problems is plotted on a 2015 AMC 8 Problems grid. What fraction of the grid is covered by the triangle?

2015 AMC 8 Problems

2015 AMC 8 Problems

 

Problem 20

Ralph went to the store and bought 2015 AMC 8 Problems pairs of socks for a total of 2015 AMC 8 Problems. Some of the socks he bought cost 2015 AMC 8 Problems a pair, some of the socks he bought cost 2015 AMC 8 Problems a pair, and some of the socks he bought cost 2015 AMC 8 Problems a pair. If he bought at least one pair of each type, how many pairs of 2015 AMC 8 Problems socks did Ralph buy?

2015 AMC 8 Problems

 

Problem 21

In the given figure hexagon 2015 AMC 8 Problems is equiangular, 2015 AMC 8 Problems and 2015 AMC 8 Problems are squares with areas 2015 AMC 8 Problems and 2015 AMC 8 Problems respectively, 2015 AMC 8 Problems is equilateral and 2015 AMC 8 Problems. What is the area of 2015 AMC 8 Problems?

2015 AMC 8 Problems

2015 AMC 8 Problems

 

Problem 22

On June 2015 AMC 8 Problems, a group of students are standing in rows, with 2015 AMC 8 Problems students in each row. On June 2015 AMC 8 Problems, the same group is standing with all of the students in one long row. On June 2015 AMC 8 Problems, the same group is standing with just one student in each row. On June 2015 AMC 8 Problems, the same group is standing with 2015 AMC 8 Problems students in each row. This process continues through June 2015 AMC 8 Problems with a different number of students per row each day. However, on June 2015 AMC 8 Problems, they cannot find a new way of organizing the students. What is the smallest possible number of students in the group?

2015 AMC 8 Problems

 

Problem 23

Tom has twelve slips of paper which he wants to put into five cups labeled 2015 AMC 8 Problems, 2015 AMC 8 Problems, 2015 AMC 8 Problems, 2015 AMC 8 Problems, 2015 AMC 8 Problems. 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 2015 AMC 8 Problems to 2015 AMC 8 Problems. The numbers on the papers are 2015 AMC 8 Problems and 2015 AMC 8 Problems. If a slip with 2015 AMC 8 Problems goes into cup 2015 AMC 8 Problems and a slip with 2015 AMC 8 Problems goes into cup 2015 AMC 8 Problems, then the slip with 2015 AMC 8 Problems must go into what cup?

2015 AMC 8 Problems

 

Problem 24

A baseball league consists of two four-team divisions. Each team plays every other team in its division 2015 AMC 8 Problems games. Each team plays every team in the other division 2015 AMC 8 Problems games with 2015 AMC 8 Problems and 2015 AMC 8 Problems. Each team plays a 2015 AMC 8 Problems-game schedule. How many games does a team play within its own division?

2015 AMC 8 Problems

 

Problem 25

One-inch squares are cut from the corners of this 2015 AMC 8 Problems inch square. What is the area in square inches of the largest square that can be fitted into the remaining space?

2015 AMC 8 Problems

2015 AMC 8 Problems

 

 

 

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