2010 AMC 8 真题与答案解析

2010 AMC 8 真题

答案详细解析请参考文末

Problem 1

At Euclid Middle School the mathematics teachers are Miss Germain, Mr. Newton, and Mrs. Young. There are 2010 AMC 8 Problems students in Mrs. Germain's class, 2010 AMC 8 Problems students in Mr. Newton's class, and 2010 AMC 8 Problems students in Mrs. Young's class taking the AMC 8 this year. How many mathematics students at Euclid Middle School are taking the contest?

2010 AMC 8 Problems

 

Problem 2

If 2010 AMC 8 Problems for 2010 AMC 8 Problems positive integers, then what is 2010 AMC 8 Problems?

2010 AMC 8 Problems

 

Problem 3

The graph shows the price of five gallons of gasoline during the first ten months of the year. By what percent is the highest price more than the lowest price?

2010 AMC 8 Problems

2010 AMC 8 Problems

 

Problem 4

What is the sum of the mean, median, and mode of the numbers 2010 AMC 8 Problems?

2010 AMC 8 Problems

 

Problem 5

Alice needs to replace a light bulb located 2010 AMC 8 Problems centimeters below the ceiling in her kitchen. The ceiling is 2010 AMC 8 Problems meters above the floor. Alice is 2010 AMC 8 Problems meters tall and can reach 2010 AMC 8 Problems centimeters above the top of her head. Standing on a stool, she can just reach the light bulb. What is the height of the stool, in centimeters?

2010 AMC 8 Problems

 

Problem 6

Which of the following figures has the greatest number of lines of symmetry?

2010 AMC 8 Problems 2010 AMC 8 Problems 2010 AMC 8 Problems 2010 AMC 8 Problems 2010 AMC 8 Problems

 

Problem 7

Using only pennies, nickels, dimes, and quarters, what is the smallest number of coins Freddie would need so he could pay any amount of money less than a dollar?

2010 AMC 8 Problems

 

Problem 8

As Emily is riding her bicycle on a long straight road, she spots Emerson skating in the same direction 2010 AMC 8 Problems mile in front of her. After she passes him, she can see him in her rear mirror until he is 2010 AMC 8 Problems mile behind her. Emily rides at a constant rate of 2010 AMC 8 Problems miles per hour, and Emerson skates at a constant rate of 2010 AMC 8 Problems miles per hour. For how many minutes can Emily see Emerson?

2010 AMC 8 Problems

 

Problem 9

Ryan got 2010 AMC 8 Problems of the problems correct on a 2010 AMC 8 Problems-problem test, 2010 AMC 8 Problems on a 2010 AMC 8 Problems-problem test, and 2010 AMC 8 Problems on a 2010 AMC 8 Problems-problem test. What percent of all the problems did Ryan answer correctly?

2010 AMC 8 Problems

 

Problem 10

Six pepperoni circles will exactly fit across the diameter of a 2010 AMC 8 Problems-inch pizza when placed. If a total of 2010 AMC 8 Problems circles of pepperoni are placed on this pizza without overlap, what fraction of the pizza is covered by pepperoni?

2010 AMC 8 Problems

 

Problem 11

The top of one tree is 2010 AMC 8 Problems feet higher than the top of another tree. The heights of the two trees are in the ratio 2010 AMC 8 Problems. In feet, how tall is the taller tree?

2010 AMC 8 Problems

 

Problem 12

Of the 2010 AMC 8 Problems balls in a large bag, 2010 AMC 8 Problems are red and the rest are blue. How many of the red balls must be removed from the bag so that 2010 AMC 8 Problems of the remaining balls are red?

2010 AMC 8 Problems

 

Problem 13

The lengths of the sides of a triangle in inches are three consecutive integers. The length of the shortest side is 2010 AMC 8 Problems of the perimeter. What is the length of the longest side?

2010 AMC 8 Problems

 

Problem 14

What is the sum of the prime factors of 2010 AMC 8 Problems?

2010 AMC 8 Problems

 

Problem 15

A jar contains five different colors of gumdrops: 2010 AMC 8 Problems are blue, 2010 AMC 8 Problems are brown, 2010 AMC 8 Problems red, 2010 AMC 8 Problems yellow, and the other 2010 AMC 8 Problems gumdrops are green. If half of the blue gumdrops are replaced with brown gumdrops, how many gumdrops will be brown?

2010 AMC 8 Problems

 

Problem 16

A square and a circle have the same area. What is the ratio of the side length of the square to the radius of the circle?

2010 AMC 8 Problems

 

Problem 17

The diagram shows an octagon consisting of 2010 AMC 8 Problems unit squares. The portion below 2010 AMC 8 Problems is a unit square and a triangle with base 2010 AMC 8 Problems. If 2010 AMC 8 Problems bisects the area of the octagon, what is the ratio 2010 AMC 8 Problems?

2010 AMC 8 Problems

2010 AMC 8 Problems

 

Problem 18

A decorative window is made up of a rectangle with semicircles on either end. The ratio of 2010 AMC 8 Problems to 2010 AMC 8 Problems is 2010 AMC 8 Problems, and 2010 AMC 8 Problems is 30 inches. What is the ratio of the area of the rectangle to the combined areas of the semicircles?

2010 AMC 8 Problems

2010 AMC 8 Problems

 

Problem 19

The two circles pictured have the same center 2010 AMC 8 Problems. Chord 2010 AMC 8 Problems is tangent to the inner circle at 2010 AMC 8 Problems, 2010 AMC 8 Problems is 2010 AMC 8 Problems, and chord 2010 AMC 8 Problems has length 2010 AMC 8 Problems. What is the area between the two circles?

2010 AMC 8 Problems

2010 AMC 8 Problems

 

Problem 20

In a room, 2010 AMC 8 Problems of the people are wearing gloves, and 2010 AMC 8 Problems of the people are wearing hats. What is the minimum number of people in the room wearing both a hat and a glove?

2010 AMC 8 Problems

 

Problem 21

Hui is an avid reader. She bought a copy of the best seller Math is Beautiful. On the first day, Hui read 2010 AMC 8 Problems of the pages plus 2010 AMC 8 Problems more, and on the second day she read 2010 AMC 8 Problems of the remaining pages plus 2010 AMC 8 Problems pages. On the third day she read 2010 AMC 8 Problems of the remaining pages plus 2010 AMC 8 Problems pages. She then realized that there were only 2010 AMC 8 Problems pages left to read, which she read the next day. How many pages are in this book?

2010 AMC 8 Problems

 

Problem 22

The hundreds digit of a three-digit number is 2010 AMC 8 Problems more than the units digit. The digits of the three-digit number are reversed, and the result is subtracted from the original three-digit number. What is the units digit of the result?

2010 AMC 8 Problems

 

Problem 23

Semicircles 2010 AMC 8 Problems and 2010 AMC 8 Problems pass through the center 2010 AMC 8 Problems. What is the ratio of the combined areas of the two semicircles to the area of circle 2010 AMC 8 Problems? 2010 AMC 8 Problems

2010 AMC 8 Problems

 

Problem 24

What is the correct ordering of the three numbers, 2010 AMC 8 Problems, 2010 AMC 8 Problems, and 2010 AMC 8 Problems?

2010 AMC 8 Problems

2010 AMC 8 Problems

2010 AMC 8 Problems

2010 AMC 8 Problems

2010 AMC 8 Problems

 

Problem 25

Everyday at school, Jo climbs a flight of 2010 AMC 8 Problems stairs. Jo can take the stairs 2010 AMC 8 Problems, 2010 AMC 8 Problems, or 2010 AMC 8 Problems at a time. For example, Jo could climb 2010 AMC 8 Problems, then 2010 AMC 8 Problems, then 2010 AMC 8 Problems. In how many ways can Jo climb the stairs?

2010 AMC 8 Problems

 

 

 

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