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2025 AMC 12B problems

All 25 problems from the 2025 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 1The instructions on a 350-gram bag of coffee beans say that proper brewing of a large mug of pour-over coffee requires 20 grams of coffee beans. What…Algebra
  2. 2Problem 2Jerry wrote down the ones digit of each of the first 2025 positive squares: 1, 4, 9, 6, 5, 6, …. What is the sum of all the numbers Jerry wrote down?Algebra
  3. 3Problem 3What is the value of i(i-1)(i-2)(i-3), where i = √(-1)?Algebra
  4. 4Problem 4The value of the two-digit number a b in base seven equals the value of the two-digit number b a in base nine. What is a + b?Algebra
  5. 5Problem 5Positive integers x and y satisfy the equation 57x + 22y = 400. What is the least possible value of x + y?Number Theory
  6. 6Problem 6Emmy says to Max, “I ordered 36 math club sweatshirts today.” Max asks, “How much did each shirt cost?” Emmy responds, “I’ll give you a hint. The…Number Theory
  7. 7Problem 7What is the value of sum _n=2^255 log _2(1 + 1/n)/(log _2 n)(log _2(n+1))?Algebra
  8. 8Problem 8There are integers a and b such that the polynomial x^3 - 5x^2 + ax + b has 4 + √(5) as a root. What is a + b?Algebra
  9. 9Problem 9What is the tens digit of 6^6^6?Number Theory
  10. 10Problem 10The altitude to the hypotenuse of a 30-60-90 right triangle is divided into two segments of lengths x < y by the median to the shortest side of the…Geometry
  11. 11Problem 11Nine athletes, no two of whom are the same height, try out for the basketball team. One at a time, they draw a wristband at random, without…Counting & Probability
  12. 12Problem 12The windshield wiper on the driver’s side of a large bus is depicted below. Arm AB pivots back and forth around point A, sweeping out an arc of 60°…Geometry
  13. 13Problem 13A circle has been divided into 6 sectors of different sizes. Then 2 of the sectors are painted red, 2 painted green, and 2 painted blue so that no…Counting & Probability
  14. 14Problem 14Consider a decreasing sequence of n positive integers x_1 > x_2 > … > x_n that satisfies the following two conditions: • The average (arithmetic…Algebra
  15. 15Problem 15A container has a 1 × 1 square bottom, a 3 × 3 open square top, and four congruent trapezoidal sides, as shown. Starting when the container is empty…Geometry
  16. 16Problem 16An analog clock starts at midnight and runs for 2025 minutes before stopping. What is the tangent of the acute angle between the hour hand and the…Algebra
  17. 17Problem 17Each of the 9 squares in a 3 × 3 grid is to be colored red, blue, or yellow in such a way that each red square shares an edge with at least one blue…Counting & Probability
  18. 18Problem 18Awnik repeatedly plays a game that has a probability of winning of 1/3. The outcomes of the games are independent. What is the expected value of the…Counting & Probability
  19. 19Problem 19A rectangular grid of squares has 141 rows and 91 columns. Each square has room for two numbers. Horace and Vera each fill in the grid by putting the…Number Theory
  20. 20Problem 20A frog hops along the number line according to the following rules. • It starts at 0. • If it is at 0, then it moves to 1 with probability 1/2 and it…Counting & Probability
  21. 21Problem 21Two non-congruent triangles have the same area. Each triangle has sides of length 8 and 9, and the third side of each triangle has integer length…Geometry
  22. 22Problem 22What is the greatest possible area of the triangle in the complex plane with vertices 2z, (1+i)z, and (1-i)z, where z is a complex number satisfying…Algebra
  23. 23Problem 23Let S be the set of all integers z > 1 such that for all pairs of nonnegative integers (x, y) with x < y < z, the remainder when 2025x is divided by…Number Theory
  24. 24Problem 24How many real numbers satisfy the equation sin (20π x) = log _20(x)?Algebra
  25. 25Problem 25Three concentric circles have radii 1, 2, 3. An equilateral triangle with side length s has one vertex on each circle. What is s^2?Geometry

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