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2025 AMC 12A problems

All 25 problems from the 2025 AMC 12A, 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 1Andy and Betsy both live in Mathville. Andy leaves Mathville on his bicycle at 1:30, traveling due north at a steady 8 miles per hour. Betsy leaves…Algebra
  2. 2Problem 2A box contains 10 pounds of a nut mix that is 50 percent peanuts, 20 percent cashews, and 30 percent almonds. A second nut mix containing 20 percent…Algebra
  3. 3Problem 3A team of students is going to compete against a team of teachers in a trivia contest. The total number of students and teachers is 15. Ash, a cousin…Algebra
  4. 4Problem 4Agnes writes the following four statements on a blank piece of paper. • At least one of these statements is true. • At least two of these statements…
  5. 5Problem 5In the figure below, the outside square contains infinitely many squares, each of them with the same center and sides parallel to the outside square…Algebra
  6. 6Problem 6Six chairs are arranged around a round table. Two students and two teachers randomly select four of the chairs to sit in. What is the probability…Counting & Probability
  7. 7Problem 7In a certain alien world, the maximum running speed v of an organism is dependent on its number of toes n and number of eyes m. The relationship can…Algebra
  8. 8Problem 8Pentagon ABCDE is inscribed in a circle, and ∠ BEC = ∠ CED = 30°. Let AC and BD intersect at point F, and suppose that AB = 9 and AD = 24. What is BF?Geometry
  9. 9Problem 9Let w be the complex number 2 + i, where i = √(-1). What real number r has the property that r, w, and w^2 are three collinear points in the complex…Algebra
  10. 10Problem 10In the figure shown below, major arc AD and minor arc BC have the same center, O. Also, A lies between O and B, and D lies between O and C. Major arc…Algebra
  11. 11Problem 11The orthocenter of a triangle is the concurrent intersection of the three (possibly extended) altitudes. What is the sum of the coordinates of the…Geometry
  12. 12Problem 12The harmonic mean of a collection of numbers is the reciprocal of the arithmetic mean of the reciprocals of the numbers in the collection. For…Algebra
  13. 13Problem 13Let C = {1, 2, 3, …, 13}. Let N be the greatest integer such that there exists a subset of C with N elements that does not contain five consecutive…Counting & Probability
  14. 14Problem 14Points F, G, and H are collinear with G between F and H. The ellipse with foci at G and H is internally tangent to the ellipse with foci at F and G…Geometry
  15. 15Problem 15A set of numbers is called sum-free if whenever x and y are (not necessarily distinct) elements of the set, x + y is not an element of the set. For…Algebra
  16. 16Problem 16Triangle △ ABC has side lengths AB = 80, BC = 45, and AC = 75. The bisector of ∠ B and the altitude to side AB intersect at point P. What is BP?Geometry
  17. 17Problem 17The polynomial (z + i)(z + 2i)(z + 3i) + 10 has three roots in the complex plane, where i = √(-1). What is the area of the triangle formed by these…Algebra
  18. 18Problem 18How many ordered triples (x, y, z) of distinct nonnegative integers less than or equal to 8 satisfy xy > z, zx > y, and yz > x?Algebra
  19. 19Problem 19Let a, b, and c be the roots of the polynomial x^3 + kx + 1. What is the sum a^3b^2 + a^2b^3 + b^3c^2 + b^2c^3 + c^3a^2 + c^2a^3?Algebra
  20. 20Problem 20The base of the pentahedron shown below is a 13 × 8 rectangle, and its lateral faces are two isosceles triangles with base of length 8 and congruent…Geometry
  21. 21Problem 21There is a unique ordered triple (a, k, m) of nonnegative integers such that small frac 4^a + 4^a+k + 4^a+2k + … + 4^a+mk2^a + 2^a+k + 2^a+2k + … +…Algebra
  22. 22Problem 22Three real numbers are chosen independently and uniformly at random between 0 and 1. What is the probability that the greatest of these three numbers…Algebra
  23. 23Problem 23Call a positive integer fair if no digit is used more than once, it has no 0s, and no digit is adjacent to two greater digits. For example, 196, 23…Algebra
  24. 24Problem 24A circle of radius r is surrounded by 12 circles of radius 1, externally tangent to the central circle and sequentially tangent to each other, as…Geometry
  25. 25Problem 25Polynomials P(x) and Q(x) each have degree 3 and leading coefficient 1, and their roots are all elements of {1, 2, 3, 4, 5}. The function f(x) =…Algebra

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