2015年 AMC10 B卷
2015 AMC 10B Problems
Problem 1
What is the value of 2 - (-2)-2 ?
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?
(A) 3:10 PM (B) 3:30 PM (C) 4:00 PM (D) 4:10 PM (E) 4:30 PM
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
Four siblings ordered an extra large pizza. Alex ate , Beth , and Cyril of the pizza. Dan got the leftovers. What is the sequence of the siblings in decreasing order of the part of pizza they consumed?
(A) Alex, Beth, Cyril, Dan (B) Beth, Cyril, Alex, Dan
(C) Beth, Cyril, Dan, Alex (D) Beth, Dan, Cyril, Alex
(E) Dan, Beth, Cyril, Alex
Problem 5
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?
(A) David (B) Hikmet (C) Jack (D) Rand (E) Todd
Problem 6
Marley practices exactly one sport each day of the week. She runs three days a week but never on two consecutive days. On Monday she plays basketball and two days later golf. She swims and plays tennis, but she never plays tennis the day after running or swimming. Which day of the week does Marley swim?
(A) Sunday (B) Tuesday (C) Thursday
(D) Friday (E) Saturday
Problem 7
Consider the operation "minus the reciprocal of," defined by . What is ((1 ◇ 2) ◇ 3) - (1 ◇ (2 ◇ 3)) ?
Problem 8
The letter F shown below is rotated 90° clockwise around the origin, then reflected in the y-axis, and then rotated a half turn around the origin. What is the final image?
Problem 9
The shaded region below is called a shark's fin falcata, a figure studied by Leonardo da Vinci. It is bounded by the portion of the circle of radius 3 and center (0, 0) that lies in the first quadrant, the portion of the circle with radius and center that lies in the first quadrant, and the line segment from (0, 0) to (3, 0). What is the area of the shark's fin falcata?
Problem 10
What are the sign and units digit of the product of all the odd negative integers strictly greater than -2015?
(A) It is a negative number ending with a 1.
(B) It is a positive number ending with a 1.
(C) It is a negative number ending with a 5.
(D) It is a positive number ending with a 5.
(E) It is a negative number ending with a 0.
Problem 11
Among the positive integers less than 100, each of whose digits is a prime number, one is selected at random. What is the probability that the selected number is prime?
Problem 12
For how many integers x is the point (x, -x) inside or on the circle of radius 10 centered at (5, 5) ?
Problem 13
The line 12x + 5y = 60 forms a triangle with the coordinate axes. What is the sum of the lengths of the altitudes of this triangle?
Problem 14
Let a, b, and c be three distinct one-digit numbers. What is the maximum value of the sum of the roots of the equation (x - a)(x - b)+(x - b)(x - c) = 0 ?
Problem 15
The town of Hamlet has 3 people for each horse, 4 sheep for each cow, and 3 ducks for each person. Which of the following could not possibly be the total number of people, horses, sheep, cows, and ducks in Hamlet?
Problem 16
Al, Bill, and Cal will each randomly be assigned a whole number from 1 to 10, inclusive, with no two of them getting the same number. What is the probability that Al's number will be a whole number multiple of Bill's and Bill's number will be a whole number multiple of Cal's?
Problem 17
When the centers of the faces of the right rectangular prism shown below are joined to create an octahedron, what is the volume of the octahedron?
In the figure shown below, ABCDE is a regular pentagon and AG = 1. What is FG + JH + CD ?