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2015 AMC 10B problems

All 25 problems from the 2015 AMC 10B, with answer choices, worked solutions and hints. Problems are roughly ordered by difficulty: 1–10 are the most approachable, 19–25 the hardest.

Problems

  1. 1Problem 1What is the value of 2-(-2)^-2?Algebra
  2. 2Problem 2Marie 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…Algebra
  3. 3Problem 3Isaac 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…Algebra
  4. 4Problem 4Four siblings ordered an extra large pizza. Alex ate frac 15, Beth frac 13, and Cyril frac 14 of the pizza. Dan got the leftovers. What is the…Algebra
  5. 5Problem 5David, 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…
  6. 6Problem 6Marley 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…
  7. 7Problem 7Consider the operation “minus the reciprocal of,” defined by a◆ b=a-1/b. What is ((1diamond 2)diamond 3)-(1◆(2diamond 3))?Algebra
  8. 8Problem 8The 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…Geometry
  9. 9Problem 9The 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…Geometry
  10. 10Problem 10What are the sign and units digit of the product of all the odd negative integers strictly greater than -2015?Number Theory
  11. 11Problem 11Among 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…Counting & Probability
  12. 12Problem 12For how many integers x is the point (x, -x) inside or on the circle of radius 10 centered at (5, 5)?Geometry
  13. 13Problem 13The line 12x+5y=60 forms a triangle with the coordinate axes. What is the sum of the lengths of the altitudes of this triangle?Geometry
  14. 14Problem 14Let 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?Algebra
  15. 15Problem 15The 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…Number Theory
  16. 16Problem 16Al, 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…Counting & Probability
  17. 17Problem 17The centers of the faces of the right rectangular prism shown below are joined to create an octahedron. What is the volume of this octahedron?Geometry
  18. 18Problem 18Johann has 64 fair coins. He flips all the coins. Any coin that lands on tails is tossed again. Coins that land on tails on the second toss are…Counting & Probability
  19. 19Problem 19In △ABC, ∠C = 90^° and AB = 12. Squares ABXY and ACWZ are constructed outside of the triangle. The points X, Y, Z, and W lie on a circle. What is the…Geometry
  20. 20Problem 20Erin the ant starts at a given corner of a cube and crawls along exactly 7 edges in such a way that she visits every corner exactly once and then…Geometry
  21. 21Problem 21Cozy 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…Algebra
  22. 22Problem 22In the figure shown below, ABCDE is a regular pentagon and AG=1. What is FG + JH + CD?Geometry
  23. 23Problem 23Let n be a positive integer greater than 4 such that the decimal representation of n! ends in k zeros and the decimal representation of (2n)! ends in…Number Theory
  24. 24Problem 24Aaron the ant walks on the coordinate plane according to the following rules. He starts at the origin p_0=(0,0) facing to the east and walks one…Geometry
  25. 25Problem 25A rectangular box measures a × b × c, where a, b, and c are integers and 1≤ a ≤ b ≤ c. The volume and the surface area of the box are numerically…Algebra

Practise the same ideas across every year on the topic pages, or browse the full AMC 10 archive.