Competition · AMC preparation · step 4 of 4

AMC 8 2025: all 25 problems

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

AMC 8 2025 #1 grade 6+ geometry-2d
The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire 4×4 grid is…
AMC 8 2025 #2 grade 4+ arithmetic
The table below shows the ancient Egyptian hieroglyphs that were used to represent different numbers. For example, the n…
AMC 8 2025 #3 grade 3+ arithmetic
Buffalo Shuffle-o is a card game in which all the cards are distributed evenly among all players at the start of the gam…
AMC 8 2025 #4 grade 4+ arithmetic
Lucius is counting backward by 7s. His first three numbers are 100, 93, and 86. What is his 10th number?
AMC 8 2025 #5 grade 3+ geometry-2d
Betty drives a truck to deliver packages in a neighborhood whose street map is shown below. Betty starts at the factory…
AMC 8 2025 #6 grade 4+ number-theory
Sekou writes the numbers 15, 16, 17, 18, 19. After he erases one of his numbers, the sum of the remaining four numbers i…
AMC 8 2025 #7 grade 2+ arithmetic
On the most recent exam on Prof. Xochi's class, 5 students earned a score of at least 95%, 13 students earned a score of…
AMC 8 2025 #8 grade 8+ geometry-3d
Isaiah cuts open a cardboard cube along some of its edges to form the flat shape shown on the right, which has an area o…
AMC 8 2025 #9 grade 6+ arithmetic
Ningli looks at the 6 pairs of numbers directly across from each other on a clock. She takes the average of each pair of…
AMC 8 2025 #10 grade 5+ geometry-2d
In the figure below, ABCD is a rectangle with sides of length AB = 5 inches and AD = 3 inches. Rectangle ABCD is rotated…
AMC 8 2025 #11 grade 3+ geometry-2d, counting
A tetromino consists of four squares connected along their edges. There are five possible tetromino shapes, I, O, L, T,…
AMC 8 2025 #12 grade 8+ geometry-2d
The region shown below consists of 24 squares, each with side length 1 centimeter. What is the area, in square centimete…
AMC 8 2025 #13 grade 4+ number-theory
Each of the even numbers 2, 4, 6, …, 50 is divided by 7. The remainders are recorded. Which histogram displays the numbe…
AMC 8 2025 #14 grade 6+ arithmetic
A number N is inserted into the list 2, 6, 7, 7, 28. The mean is now twice as great as the median. What is N?
AMC 8 2025 #15 grade 6+ counting, algebra
Kei draws a 6-by-6 grid. He colors 13 of the unit squares silver and the remaining squares gold. Kei then folds the grid…
AMC 8 2025 #16 grade 4+ counting, arithmetic
Five distinct integers from 1 to 10 are chosen, and five distinct integers from 11 to 20 are chosen. No two numbers diff…
AMC 8 2025 #17 grade 5+ rate-ratio, arithmetic
In the land of Markovia, there are three cities: A, B, and C. There are 100 people who live in A, 120 who live in B, and…
AMC 8 2025 #18 grade 7+ geometry-2d
The circle shown below on the left has a radius of 1 unit. The region between the circle and the inscribed square is sha…
AMC 8 2025 #19 grade 6+ rate-ratio
Two towns, A and B, are connected by a straight road, 15 miles long. Traveling from town A to town B, the speed limit ch…
AMC 8 2025 #20 grade 6+ rate-ratio, algebra
Sarika, Dev, and Rajiv are sharing a large block of cheese. They take turns cutting off half of what remains and eating…
AMC 8 2025 #21 grade 6+ logic, counting
The Konigsberg School has assigned grades 1 through 7 to pods A through G, one grade per pod. Some of the pods are conne…
AMC 8 2025 #22 grade 4+ number-theory, algebra
A classroom has a row of 35 coat hooks. Paulina likes coats to be equally spaced, so that there is the same number of em…
AMC 8 2025 #23 grade 5+ number-theory
How many four-digit numbers have all three of the following properties? (I) The tens and ones digit are both 9. (II) The…
AMC 8 2025 #24 grade 7+ geometry-2d, number-theory
In trapezoid ABCD, angles B and C measure 60° and AB = DC. The side lengths are all positive integers, and the perimeter…
AMC 8 2025 #25 grade 8+ counting, geometry-2d
Makayla finds all the possible ways to draw a path in a 5 × 5 diamond-shaped grid. Each path starts at the bottom of the…

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