Competition · AMC preparation · step 4 of 4

AMC 12 2025B: all 25 problems

Each problem has a solution worked from first principles and the first grade (by CCSS standards) that can solve it.

AMC 12 2025B #1 grade 5+ arithmetic
The instructions on a 350-gram bag of coffee beans say that proper brewing of a large mug of pour-over coffee requires 2…
AMC 12 2025B #2 grade 5+ number-theory
Jerry 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…
AMC 12 2025B #3 grade 11+ algebra
What is the value of i(i-1)(i-2)(i-3), where i = √(-1)?
AMC 12 2025B #4 grade 8+ number-theory
The 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…
AMC 12 2025B #5 grade 7+ number-theory
Positive integers x and y satisfy the equation 57x+ 22y = 400. What is the least possible value of x+y?
AMC 12 2025B #6 grade 6+ number-theory
Emmy says to Max, "I ordered 36 math club sweatshirts today." Max asks, "How much did each shirt cost?" Emmy responds, "…
AMC 12 2025B #7 grade 11+ algebra
What is the value of sum_(n = 2)²⁵⁵(log₂(1 + 1/n))/(log₂n)(log₂(n + 1))?
AMC 12 2025B #8 grade 11+ algebra
There are integers a and b such that the polynomial x³ - 5x² + ax + b has 4+√5 as a root. What is a+b?
AMC 12 2025B #9 grade 8+ number-theory
What is the tens digit of 6^6⁶?
AMC 12 2025B #10 grade 8+ geometry-2d
The altitude to the hypotenuse of a 30°-60°-90° is divided into two segments of lengths x<y by the median to the shortes…
AMC 12 2025B #11 grade 7+ probability
Nine athletes, no two of whom are the same height, try out for the basketball team. One at a time, they draw a wristband…
AMC 12 2025B #12 grade 10+ geometry-2d
The windshield wiper on the driver's side of a large bus is depicted below. Arm AB pivots back and forth around point A,…
AMC 12 2025B #13 grade 7+ counting
A circle has been divided into 6 sectors of different sizes. Then 2 of the sectors are painted red, 2 painted green, and…
AMC 12 2025B #14 grade 6+ algebra
Consider a decreasing sequence of n positive integers x₁ > x₂ > … > x_n that satisfies the following conditions: The ave…
AMC 12 2025B #15 grade 7+ geometry-3d
A container has a 1× 1 square bottom, a 3× 3 open square top, and four congruent trapezoidal sides, as shown. Starting w…
AMC 12 2025B #16 grade 10+ geometry-2d, rate-ratio
An analog clock starts at midnight and runs for 2025 minutes before stopping. What is the tangent of the acute angle bet…
AMC 12 2025B #17 grade 8+ counting
Each 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…
AMC 12 2025B #18 grade 12+ probability
Awnik repeatedly plays a game that has a probability of winning of 1/3. The outcomes of the games are independent. What…
AMC 12 2025B #19 grade 7+ number-theory
A rectangular grid of squares has 141 rows and 91 columns. Each square has room for two numbers. Horace and Vera each fi…
AMC 12 2025B #20 grade 8+ probability
A 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 wi…
AMC 12 2025B #21 grade 11+ geometry-2d
Two non-congruent triangles have the same area. Each triangle has sides of length 8 and 9, and the third side of each tr…
AMC 12 2025B #22 grade 11+ algebra, geometry-2d
What 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…
AMC 12 2025B #23 grade 7+ number-theory
Let S be the set of all integers z > 1 such that for all pairs of nonnegative integers (x, y) with x < y < z, the remain…
AMC 12 2025B #24 grade 11+ algebra
How many real numbers satisfy the equation sin(20π x) = log₂₀(x)?
AMC 12 2025B #25 grade 11+ geometry-2d
Three concentric circles have radii 1, 2, and 3. An equilateral triangle of side length s has one vertex on each circle.…

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