AMC8 Mock Test

2026

Arithmetic & Operations

1

What is the value of the following expression? 1 + 2 − 3 + 4 + 5 − 6 + 7 + 8 − 9 + 10 + 11 − 12

2026

Arithmetic & Operations

2

In the array shown, three 3s are surrounded by 2s, which are in turn surrounded by a border of 1s. What is the sum of the numbers in the array?

2026

Geometry & Measurement

3

Haruki has a piece of wire that is 24 cm long. He wants to bend it to form each of the following shapes, one at a time: a regular hexagon with side length 5 cm; a square of area 36 cm²; and a right triangle whose legs are 6 cm and 8 cm long. Which shapes can he make?

2026

Fractions, Decimals & Percents

4

Brynn’s savings decreased by 20% in July, then increased by 50% in August. What percent of the original amount does Brynn have now?

2026

Ratios, Rates & Proportions

5

Casey went on a road trip that covered 100 miles, stopping only for a lunch break along the way. The trip took 3 hours in total, and her average speed while driving was 40 miles per hour. In minutes, how long was the lunch break?

2026

Geometry & Measurement

6

Peter lives near a rectangular field that is 10 meters long and 8 meters wide. He can reach any blackberries within 1 meter of an edge of the field, as shown in the figure. What fraction of the field’s area can Peter reach?

2026

Ratios, Rates & Proportions

7

Mika completed two trips totaling 40 miles on a new electric bike. The first trip used 1/2 of the total battery power, and the second used 3/10 of the total battery power. How many miles can the bike travel on a fully charged battery?

2026

Fractions, Decimals & Percents

8

A poll asked people whether they liked solving mathematics problems. Exactly 74% answered “yes.” What is the fewest possible number of people who could have been asked?

2026

Arithmetic & Operations

9

What is the value of this expression? √(16√81) / √(81√16)

2026

Logic & Word Problems

10

Five runners completed the Xmarathon: Luke, Melina, Nico, Olympia, and Pedro. Nico finished 11 minutes behind Pedro. Olympia finished 2 minutes ahead of Melina, but 3 minutes behind Pedro. Olympia finished 6 minutes ahead of Luke. Which runner finished fourth?

2026

Geometry & Measurement

11

Squares of side lengths 1, 1, 2, 3, and 5 are arranged to form a rectangle. A curve is made by inscribing a quarter circle in each square and joining the arcs from shortest to longest. What is the length of the curve?

2026

Algebra & Patterns

12

Each circle in the figure is filled with a digit from 1 to 6, with each digit used exactly once. The number in each box is the sum of the digits in the two neighboring circles. What digit must go in the top circle?

2026

Geometry & Measurement

13

The figure shows a tiling of 1 × 1 unit squares, with each row shifted horizontally by half a unit from the row above. Each vertex of the shaded square is a vertex of a unit square. What is the area of the shaded square, in square units?

2026

Algebra & Patterns

14

Jami picked three equally spaced integers on the number line. The sum of the first and second numbers is 40, and the sum of the second and third numbers is 60. What is the sum of all three numbers?

2026

Spatial & Visual Reasoning

15

Elijah has identical wooden cubes that are plain on 4 faces and shaded on 2 faces that share an edge. He glues cubes face-to-face. What is the fewest number of cubes needed to ensure that no shaded faces are visible, regardless of how the figure is rotated?

2026

Number Theory

16

Consider all positive four-digit integers made only from even digits. What fraction of them are divisible by 4?

2026

Counting & Probability

17

Four students sit in a row and talk with the people next to them. They rearrange themselves so that no student sits next to any of the same people as before. How many rearrangements are possible?

2026

Number Theory

18

In how many ways can 60 be written as the sum of two or more consecutive positive odd integers in increasing order?

2026

Ratios, Rates & Proportions

19

Miguel walks with his dog Luna. At a park entrance, he throws a ball straight ahead and keeps walking at a steady pace. Luna runs to the ball, which stops by a tree, then immediately runs back to Miguel. Luna runs 5 times as fast as Miguel. What fraction of the distance from the entrance to the tree does Miguel walk before Luna returns?

2026

Counting & Probability

20

Gold coins are 1 mm thick and silver coins are 3 mm thick. In how many ways can Taylor make a stack exactly 8 mm tall, using any order of the coins? The order of the coins matters.

2026

Counting & Probability

21

Charlotte the spider walks on the 5-pointed star web shown. The web has 5 outer points and 5 inner points. At each point, she randomly chooses a neighboring point and moves there. Starting at an outer point, she makes 3 moves; revisiting points is allowed. What is the probability she is at an outer point after the third move?

2026

Logic & Word Problems

22

The integers 1 through 25 are divided into five groups of 5 numbers each. The median of each group is found, and M is the median of those five medians. What is the least possible value of M?

2026

Geometry & Measurement

23

Lakshmi has 5 round coins, each 4 cm in diameter, arranged in 2 rows as shown. She wraps a tight elastic band around them. What is the length of the band, in centimeters?

2026

Number Theory

24

For a positive integer n, n! is the product of the integers from 1 to n. The superfactorial of n, written n^!, is 1! × 2! × … × n!. How many factors of 7 are in the prime factorization of 51^!?

2026

Geometry & Measurement

25

An equiangular hexagon has interior angles of 120°. The example shown is inscribed in equilateral triangle ABC. Consider all equiangular hexagons with positive integer side lengths that can be inscribed in ABC, with all six vertices on the sides of the triangle. Hexagons that differ only by a rotation or reflection count as the same. How many such hexagons are there?