AMC8 Mock Test

The eight-pointed star shown in the figure is a popular quilting pattern. What percent of the entire 4-by-4 grid is covered by the star?

The table shows ancient Egyptian hieroglyphs for different numbers. For example, 32 was represented by three tens and two ones. What number is represented by the following combination: one 10,000 symbol, four 100 symbols, two 10 symbols, and three 1 symbols?

Buffalo Shuffle-o deals all cards evenly among the players. When Annika and 3 friends play, each player gets 15 cards. If 2 more friends join the next game, how many cards will each player get?

Lucius counts backward by 7s. His first three numbers are 100, 93, and 86. What is his 10th number?

Betty drives a truck through a neighborhood whose street map is shown. Starting at factory F, she visits A, then B, then C, and returns to F. What is the shortest distance, in blocks, for the complete route?

Sekou writes 15, 16, 17, 18, and 19. After erasing one number, the sum of the remaining four is a multiple of 4. Which number did he erase?

On Prof. Xochi’s exam, 5 students scored at least 95%, 13 at least 90%, 27 at least 85%, and 50 at least 80%. How many students scored at least 80% and less than 90%?

Isaiah cuts open a cardboard cube along some edges to make the flat shape shown. The shape has area 18 square centimeters. What is the volume of the cube, in cubic centimeters?

Ningli pairs the six pairs of numbers directly opposite each other on a clock and finds each pair’s average. What is the average of those six averages?

Rectangle ABCD has side lengths AB = 5 inches and AD = 3 inches. It is rotated 90° clockwise about the midpoint of side DC to form a second rectangle. What total area is covered by the two rectangles?

Three tetrominoes completely cover a 3 × 4 rectangle. The five possible tetromino shapes are I, O, L, T, and S, and at least one tile is S. What are the other two tiles?

The region shown consists of 24 unit squares. What is the area of the largest circle that can fit inside the region, possibly touching its boundary?

Each even number from 2 through 50 is divided by 7, and the remainders are recorded. Which histogram shows the number of occurrences of each remainder?

A number N is inserted into the list 2, 6, 7, 7, 28. The mean is now twice the median. What is N?

Kei colors 13 squares silver in a 6-by-6 grid and the rest gold, then folds the grid vertically into 18 overlapping pairs. Let m and M be the least and greatest possible numbers of gold-on-gold pairs. What is m + M?

Five distinct integers are chosen from 1 to 10 and five distinct integers from 11 to 20. No two chosen numbers differ by exactly 10. What is the sum of the ten chosen numbers?

In Markovia, 100 people live in A, 120 in B, and 160 in C. Everyone works in one of the three cities, possibly the city where they live. The directed arrows show the fraction of residents of each city who work in each other city. How many people work in A?

The left circle has radius 1, and the region between it and its inscribed square is shaded. In the right circle, one quarter of the region between the circle and its inscribed square is shaded. The shaded areas are equal. What is the radius R of the right circle?

Towns A and B are 15 miles apart. From A to B, the speed limit changes every 5 miles: 25, then 40, then 20 mph. Cars start at A and B at the same time and drive at the local speed limit. How far from A do they meet?

Sarika, Dev, and Rajiv take turns eating half of the remaining cheese, starting with Sarika, and continue until it is too small to see. About what fraction of the original block does Sarika eat in total?

Grades 1 through 7 are assigned one each to pods A through G. Walkways connect some pods as shown, and connected pods must differ in grade by at least 2. What is the sum of the grades assigned to C, E, and F?

A row has 35 coat hooks. Coats are equally spaced, with the same number of empty hooks before the first coat, after the last coat, and between consecutive coats. There is at least one coat and one empty hook. How many different numbers of coats are possible?

How many four-digit numbers have tens and ones digits both 9, are 1 less than a perfect square, and are the product of exactly two primes?

In trapezoid ABCD, angles B and C are 60°, AB = DC, all side lengths are positive integers, and the perimeter is 30. How many noncongruent trapezoids satisfy these conditions?

Makayla draws every possible path through a 5 × 5 diamond-shaped grid, from bottom to top, moving one unit northeast or northwest at each step. For each path, she finds the area between it and the right side of the grid. What is the sum of these areas?