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2025 AMC 10A problems

All 25 problems from the 2025 AMC 10A, 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 3How many isosceles triangles are there with positive area whose side lengths are all positive integers and whose longest side has length 2025?Geometry
  4. 4Problem 4A 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
  5. 5Problem 5Consider the sequence of positive integers 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, … What is…Number Theory
  6. 6Problem 6In an equilateral triangle each interior angle is trisected by a pair of rays. The intersection of the interiors of the middle 20°-angle at each…Geometry
  7. 7Problem 7Suppose a and b are real numbers. When the polynomial x^3 + x^2 + ax + b is divided by x - 1, the remainder is 4. When the polynomial is divided by x…Algebra
  8. 8Problem 8Agnes 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…
  9. 9Problem 9Let f(x) = 100x^3 - 300x^2 + 200x. For how many real numbers a does the graph of y = f(x - a) pass through the point (1, 25)?Algebra
  10. 10Problem 10A semicircle has diameter AB and chord CD of length 16 parallel to AB. A smaller semicircle with diameter on AB and tangent to CD is cut from the…Geometry
  11. 11Problem 11The sequence 1, x, y, z is arithmetic. The sequence 1, p, q, z is geometric. Both sequences are strictly increasing and contain only integers, and z…Algebra
  12. 12Problem 12Carlos uses a 4-digit passcode to unlock his computer. In his passcode, exactly one digit is even, exactly one (possibly different) digit is prime…Counting & Probability
  13. 13Problem 13In 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
  14. 14Problem 14Six 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
  15. 15Problem 15In the figure below, ABEF is a rectangle, AD ⊥ DE, AF = 7, AB = 1, and AD = 5. What is the area of △ ABC?Geometry
  16. 16Problem 16There are three jars. Each of three coins is placed in one of the three jars, chosen at random and independently of the placements of the other…Counting & Probability
  17. 17Problem 17Let N be the unique positive integer such that dividing 273436 by N leaves a remainder of 16, and dividing 272760 by N leaves a remainder of 15. What…Number Theory
  18. 18Problem 18The 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
  19. 19Problem 19An array of numbers is constructed beginning with the numbers -1, 3, 1 in the top row. Each adjacent pair of numbers is summed to produce a number in…Algebra
  20. 20Problem 20A silo (right circular cylinder) with diameter 20 meters stands in a field. MacDonald is located 20 meters west and 15 meters south of the center of…Geometry
  21. 21Problem 21A 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…Counting & Probability
  22. 22Problem 22A circle of radius r is surrounded by three circles, whose radii are 1, 2, and 3, all externally tangent to the inner circle and externally tangent…Geometry
  23. 23Problem 23Triangle △ 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
  24. 24Problem 24Call 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, 23, 196…Algebra
  25. 25Problem 25A point P is chosen at random inside square ABCD. The probability that AP is neither the shortest nor the longest side of △ APB can be written as a +…Geometry

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