# 2015年AMC12B竞赛真题及答案

2015 AMC 12B 竞赛真题
Problem 1
What is the value of ?

Problem 2
Marie does three equally time-consuming tasks in a row without taking breaks. She begins the first task at 1:00 PM and finishes the second task at 2:40 PM. When does she finish the third task?

Problem 3
Isaac has written down one integer two times and another integer three times. The sum of the five numbers is 100, and one of the numbers is 28. What is the other number?

Problem 4
David, Hikmet, Jack, Marta, Rand, and Todd were in a 12-person race with 6 other people. Rand finished 6 places ahead of Hikmet. Marta finished 1 place behind Jack. David finished 2 places behind Hikmet. Jack finished 2 places behind Todd. Todd finished 1 place behind Rand. Marta finished in 6th place. Who finished in 8th place?

Problem 5

1/8

2015 年 AMC12B

The Tigers beat the Sharks 2 out of the 3 times they played. They then played more times, and the Sharks ended up winning at least 95% of all the games played. What is the minimum possible value for ?

Problem 6
Back in 1930, Tillie had to memorize her multiplication facts from to . The multiplication table she was given had rows and columns labeled with the factors, and the products formed the body of the table. To the nearest hundredth, what fraction of the numbers in the body of the table are odd?

Problem 7
A regular 15-gon has lines of symmetry, and the smallest positive angle for which it has rotational symmetry is degrees. What is ?

Problem 8
What is the value of ?

Problem 9
Larry and Julius are playing a game, taking turns throwing a ball at a bottle sitting on a ledge. Larry throws first. The winner is the first person to knock the bottle off the ledge. At each turn the probability that a player knocks the bottle off the ledge is , independently of what has happened before. What is the probability that

Larry wins the game?
2/8 2015 年 AMC12B

Problem 10
How many noncongruent integer-sided triangles with positive area and perimeter less than 15 are neither equilateral, isosceles, nor right triangles?

Problem 11
The line forms a triangle with the coordinate axes. What is the sum of the lengths of the altitudes of this triangle?

Problem 12
Let , , and be three distinct one-digit numbers. What is the maximum value ?

of the sum of the roots of the equation

Problem 13
Quadrilateral is inscribed in a circle with and . What is ?

Problem 14
A circle of radius 2 is centered at . An equilateral triangle with side 4 has a vertex at . What is the difference between the area of the region that lies inside the circle but outside the triangle and the area of the region that lies inside the triangle but outside the circle?
3/8 2015 年 AMC12B

Problem 15
At Rachelle's school an A counts 4 points, a B 3 points, a C 2 points, and a D 1 point. Her GPA on the four classes she is taking is computed as the total sum of points divided by 4. She is certain that she will get As in both Mathematics and Science, and at least a C in each of English and History. She thinks she has a chance of getting an A in English, and a has a chance of getting an A, and a chance of getting a B. In History, she chance of getting a B, independently of

what she gets in English. What is the probability that Rachelle will get a GPA of at least 3.5?

Problem 16
A regular hexagon with sides of length 6 has an isosceles triangle attached to each side. Each of these triangles has two sides of length 8. The isosceles triangles are folded to make a pyramid with the hexagon as the base of the pyramid. What is the volume of the pyramid?

Problem 17
An unfair coin lands on heads with a probability of . When tossed times, the

probability of exactly two heads is the same as the probability of exactly three heads. What is the value of ?

4/8

2015 年 AMC12B

Problem 18
For every composite positive integer in the prime factorization of factorization of function , is , define to be the sum of the factors because the prime . What is the range of the ?

. For example, , and

Problem 19
In , and . Squares constructed outside of the triangle. The points , What is the perimeter of the triangle? , and , and are lie on a circle.

Problem 20
For every positive integer , let be the remainder obtained when is

divided by 5. Define a function recursively as follows:

What is
5/8

?
2015 年 AMC12B

Problem 21
Cozy the Cat and Dash the Dog are going up a staircase with a certain number of steps. However, instead of walking up the steps one at a time, both Cozy and Dash jump. Cozy goes two steps up with each jump (though if necessary, he will just jump the last step). Dash goes five steps up with each jump (though if necessary, he will just jump the last steps if there are fewer than 5 steps left). Suppose that Dash takes 19 fewer jumps than Cozy to reach the top of the staircase. Let denote the sum of all possible numbers of steps this staircase can have. What is the sum of the digits of ?

Problem 22
Six chairs are evenly spaced around a circular table. One person is seated in each chair. Each person gets up and sits down in a chair that is not the same chair and is not adjacent to the chair he or she originally occupied, so that again one person is seated in each chair. In how many ways can this be done?

Problem 23
A rectangular box measures , where , , and are integers and . The volume and the surface area of the box are numerically equal. How many ordered triples are possible?

Problem 24
Four circles, no two of which are congruent, have centers at and points and lie on all four circles. The radius of circle , and the radius of circle is , is , , and times the . ,

6/8

2015 年 AMC12B

Furthermore, What is

and ?

. Let

be the midpoint of

.

Problem 25
A bee starts flying from point . She flies inch due east to point . For , once the bee reaches point , she turns counterclockwise and then flies inches straight to point . When the bee reaches she is exactly integers and and ? inches away from , where , , and are positive

are not divisible by the square of any prime. What is

7/8

2015 年 AMC12B

2015 AMC 12B 竞赛真题答案

1.C 11.e 21.d

2.b 12.d 22.d

3.a 13.b 23.b

4.b 14.d 24.d

5.b 15.d 25.b

6.a 16.c

7.d 17.d

8.d 18.d

9.c 19.c

10.c 20.b

8/8

2015 年 AMC12B

2010-2015年AMC 10A和B竞赛真题及答案(英文版)_图文
2010-2015 年 AMC 10A 和 B 竞赛真题及答案 (英文版) 你好,目前,只分享了 2010-2013 年 AMC 10A 和 B 竞赛真题及答案(英文版) ,2014-2015 年的暂时还 ...
2015 AMC美国数学竞赛试题及答案
2015 AMC美国数学竞赛试题及答案_初一数学_数学_初中教育_教育专区 暂无评价|0人阅读|0次下载|举报文档2015 AMC美国数学竞赛试题及答案_初一数学_数学_初中教育_...
2016年AMC12真题及答案
2016年AMC12真题及答案_高二数学_数学_高中教育_教育专区。2016,AMC12,A,2016年美国数学竞赛A 2016 AMC12 A Problem 1 What is the value of ? Solution ...
2015 AMC 12B Problems
2015 AMC 12B Problems_数学_高中教育_教育专区。2015 AMC 12B Problems Problem...二级java考前押密试题文档贡献者 hognchen1999 贡献于2015-03-25 专题推荐 2014...
AMC 12 答案汇编(2000-2016)
AMC 12 答案汇编(2000-2016),排版质量好。AMC 12(AHSME)历年真题答案 2000 ...2000~2015年美国AMC10试... 105页 1下载券 2000年美国数学竞赛-AMC... 2...

2014年美国高中数学竞赛(AMC12)A卷试题_图文
2014年美国高中数学竞赛(AMC12)A卷试题_学科竞赛_高中教育_教育专区。2014 年...2014 年美国高中数学竞赛(AMC12)A 卷试题 文档贡献者 聚仕德 贡献于2015-10...
2000到2015年AMC 10美国数学竞赛
2000到2015年AMC 10美国数学竞赛_学科竞赛_小学教育_教育专区。美国(国际)大学生数学建模竞赛将于2015年2月5日-2月9日举行。美国大学生数学建模竞赛(MCM/ICM),...
2011年AMC 10A竞赛真题及答案(英文版)
2011年AMC 10A竞赛真题及答案(英文版)_高一数学_数学_高中教育_教育专区。2011...2011 年 AMC 10A 1/7 2011 年 AMC 10A 2/7 2011 年 AMC 10A 3/7 ...
2000到2015年AMC 10美国数学竞赛 1
2000到2015年AMC 10美国数学竞赛 1_其它考试_资格考试/认证_教育专区。2000 到...左侧 D. 前方判断题,请判断对错! 43、 载客汽车从注册登记之日起,___以内...