Skip to main content

2015 AMC 12B problems

All 25 problems from the 2015 AMC 12B, 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…Number Theory
  4. 4Problem 4David, 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…
  5. 5Problem 5The Tigers beat the Sharks 2 out of the first 3 times they played. They then played N more times, and the Sharks ended up winning at least 95% of all…Algebra
  6. 6Problem 6Back in 1930, Tillie had to memorize her multiplication facts from 0 × 0 through 12 × 12. The multiplication table she was given had rows and columns…Number Theory
  7. 7Problem 7A regular 15-gon has L lines of symmetry, and the smallest positive angle for which it has rotational symmetry is R degrees. What is L + R?Geometry
  8. 8Problem 8What is the value of (625^log _5 2015)^frac 14?Algebra
  9. 9Problem 9Larry 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…Algebra
  10. 10Problem 10How many noncongruent integer-sided triangles with positive area and perimeter less than 15 are neither equilateral, isosceles, nor right triangles?Geometry
  11. 11Problem 11The 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
  12. 12Problem 12Let 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 -…Algebra
  13. 13Problem 13Quadrilateral ABCD is inscribed in a circle with ∠ BAC = 70°, ∠ ADB = 40°, AD = 4, and BC = 6. What is AC?Geometry
  14. 14Problem 14A circle of radius 2 is centered at A. An equilateral triangle with side 4 has a vertex at A. What is the difference between the area of the region…Geometry
  15. 15Problem 15At 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…Counting & Probability
  16. 16Problem 16A 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…Geometry
  17. 17Problem 17An unfair coin lands on heads with a probability of dfrac 14. When tossed n times, the probability of exactly two heads is the same as the…Counting & Probability
  18. 18Problem 18For every composite positive integer n, define r(n) to be the sum of the factors in the prime factorization of n. For example, r(50) = 12 because the…Algebra
  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…Geometry
  20. 20Problem 20For every positive integer n, let mod_5(n) be the remainder obtained when n is divided by 5. Define a function f: {0, 1, 2, 3, …} × {0, 1, 2, 3, 4} →…Algebra
  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 22Six 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…Counting & Probability
  23. 23Problem 23A 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
  24. 24Problem 24Four circles, no two of which are congruent, have centers at A, B, C, and D, and points P and Q lie on all four circles. The radius of circle A is…Geometry
  25. 25Problem 25A bee starts flying from point P_0. She flies 1 inch due east to point P_1. For j ≥ 1, once the bee reaches point P_j, she turns 30° counterclockwise…Algebra

Practise the same ideas across every year on the topic pages, or browse the full AMC 12 archive.