Competition · AMC preparation · step 4 of 4

AMC 10 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 10 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 10 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 10 2025B #3 grade 4+ algebra
A Pascal-like triangle has 10 as the top row and 10 followed by 1 as the second row. In each subsequent row the first nu…
AMC 10 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 10 2025B #5 grade 8+ geometry-2d
In △ ABC, AB = 10, AC = 18, and ∠ B = 130°. Let O be the center of the circle containing points A, B, C. What is the deg…
AMC 10 2025B #6 grade 8+ geometry-2d
The line y = 1/3x + 1 divides the square region defined by 0 ≤ x ≤ 2 and 0 ≤ y ≤ 2 into an upper region and a lower regi…
AMC 10 2025B #7 grade 8+ geometry-2d
Frances stands 15 meters directly south of a locked gate in a fence that runs east-west. Immediately behind the fence is…
AMC 10 2025B #8 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 10 2025B #9 grade 7+ counting
How many ordered triples of integers (x, y, z) satisfy the following system of inequalities? -x-y-z ≤ -2 -x+y+z ≤ 2 x-y+…
AMC 10 2025B #10 grade 8+ algebra
Let f(n)=n³-5n²+2n+8 and g(n)=n³-6n²+5n+12. What is the sum of all integers n such that (f(n))/(g(n)) is an integer?
AMC 10 2025B #11 grade 7+ probability
On Monday, 6 students went to the tutoring center at the same time, and each one was randomly assigned to one of the 6 t…
AMC 10 2025B #12 grade 8+ geometry-2d
The figure below shows an equilateral triangle, a rhombus with a 60° angle, and a regular hexagon, each of them containi…
AMC 10 2025B #13 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 10 2025B #14 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 10 2025B #15 grade 6+ algebra
The sum sum_(k=1)^(∞) 1/(k³ + 6k² + 8k) can be expressed as a/b, where a and b are relatively prime positive integers. W…
AMC 10 2025B #16 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 10 2025B #17 grade 6+ algebra
Consider a decreasing sequence of n positive integers x₁ > x₂ > … > x_n that satisfies the following conditions: The ave…
AMC 10 2025B #18 grade 8+ number-theory
What is the ones digit of the sum ⌊ √1 ⌋ + ⌊ √2 ⌋ + ⌊ √3 ⌋ + … + ⌊ √2025 ⌋?(Recall that ⌊ x ⌋ represents the greatest in…
AMC 10 2025B #19 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 10 2025B #20 grade 8+ geometry-2d
Four congruent semicircles are inscribed in a square of side length 1 so that their diameters are on the sides of the sq…
AMC 10 2025B #21 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 10 2025B #22 grade 7+ probability
A seven-digit positive integer is chosen at random. What is the probability that the number is divisible by 11, given th…
AMC 10 2025B #23 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 10 2025B #24 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 10 2025B #25 grade 8+ geometry-2d
Square ABCD has sides of length 4. Points P and Q lie on AD and CD, respectively, with AP=8/5 and DQ=10/3. A path begins…

A parent dashboard for the family lives at sensimlab.com.