Student Name:

AMC8 2025

Mock Exam
General • This is an AMC8 Mock Test, only one attempt is allowed.
Instructions • It consists of 25 multiple-choice questions.
• The test is limited to 40 minutes.
• No calculator is allowed.
• It is a closed-book test, no reference is allowed.
• The scores are based on the number of questions answered cor-
rectly only. There is no penalty for getting a question wrong, and
each question has equal value.
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1 What is the value of the expression 0+ 25
?

A. 1
B. 2
C. 3
D. 4
E. 5

2 What is the tens digit of the result of the expression 9 + 99 + 999 + 9999 + 99999 + 999999?

A. 0
B. 1
C. 4
D. 8
E. 9

3 What is the maximum number of regions we can get by cutting the interior of a circle with 5
straight lines? We only count regions inside the circle.

A. 10
B. 16
C. 20
D. 24
E. 32

a−b
4 A new operator ⌣ is defined as a ⌣ b = a+b . What is the value of (2 ⌣ 2) ⌣ 2?

A. −2
B. −1
C. 0
D. 1
E. 2

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5 All of the regions in the following graph have the same area. The smaller circle has radius 6.
What is the radius of the larger circle?

A. 8
B. 9
C. 10
D. 11
E. 12

6 New York JFK Airport to Singapore Changi Airport is the longest commercial flight in the
world available as of 2024. It takes 18 hours and 40 minutes to complete this 9537-mile route.
Which of the following is closest to the average speed of this flight?

A. 378 mph
B. 403 mph
C. 456 mph
D. 511 mph
E. 549 mph

7 Alan, Bella and Churchill each has some red marbles and green marbles. The number of Alan’s
red marbles is 2 more than the number of green marbles of Bella. The number of Bella’s red
marbles is 3 more than the number of green marbles of Churchill. The number of Churchill’s
red marbles is 4 more than the number of green marbles of Alan. They have 109 green marbles
total. How many red marbles do they have in total?

A. 90
B. 100
C. 109

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 D. 118
E. 119

8 Seven dogs, including Luna and Milo, are going to take a picture and they sit in a row in some
random order. What is the probability that Luna is next to Milo?

1
A. 6
2
B. 7
1
C. 3
1
D. 2
5
E. 7

9 A and B are positive integers with ratio A : B = 4 : 5. Which of the following can be the ratio of
A to B if we increase both A and B by the same positive number?

A. 1:3
B. 3:5
C. 5:7
D. 7:9
E. 9 : 11

10 1,2,3,4 and 5 are arranged in increasing order from left to right. For each operation we can
swap two numbers that are next to each. How many operations do we need to perform so that
the numbers are in decreasing order from left to right?

A. 7
B. 8
C. 9
D. 10
E. 11

11 In the following graph, rectangle EFGB and rectangle HIJD cut the large rectangle ABCD into
5 regions. Region Ω1 has perimeter 17, region Ω2 has perimeter 25 and region Ω3 has perimeter
10, What is the perimeter of ABCD?

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 A. 30
B. 31
C. 32
D. 33
E. 34

12 What is the largest number of integers from 1 to 10 we can pick such that their product is a
perfect square? Each number can only be picked once.

A. 6
B. 7
C. 8
D. 9
E. 10

13 There are four points on the plane: A(−2, −5), B(−3, 6), C(4, 7) and D(−5, 8). Connect each
pair of points and we get six segments, Which segment has the longest length?

A. AB
B. AC
C. AD
D. BC
E. BD

14 A hockey game between two teams is ’super close’ if at any stage during the game the number
of goals scored by the two teams never differ by more than one. In how many ways can the first
10 goals of a game be scored if the game is ’super close’?

A. 32
B. 64
C. 128

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 D. 210
E. 1024

15 Use each integer once from 1 to 6 to form three 2-digit numbers so that their product is largest
possible. What is the remainder of this product when divided by 9?

A. 0
B. 1
C. 2
D. 3
E. 4

16 A and B are two positive integers with greatest common divisor 12. Which of the following is a
possible value of the greatest common divisor of A + 20 and B?

A. 7
B. 8
C. 13
D. 14
E. 20

17 Each time Freddy the frog can jump one step up, down, left or right. What is the number of
possible locations of Freddy after exactly 5 jumps?

A. 16
B. 20
C. 25
D. 36
E. 1024

18 The center of a disk with radius 2 is at the top-left vertex of a square with side length 4. Move
the disk so that its center moves along the sides of the square clockwise and it stops when the

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 center of the disk is at the bottom-right vertex of the square. What is the area of the region
swept by the disk?

A. 28 + 5π
B. 32 + 4π
C. 36 + 3π
D. 40 + 2π
E. 44 + π

19 In a prime-Sudoku game, the objective is to fill a 4-by-4 grid with 1, 2, 3 and 4 so that each col-
umn, each row and each of the four 2-by2 subgrids that compose the grid (also called ”boxes”)
contains all of the digits from 1 to 4 and the sum of any two numbers next to each other is a
prime number. What is A?

A. 1
B. 2
C. 3
D. 4
E. Not enough information

20 In the following graph the largest square has side length 25 and the medium square has side
length 20. The top-right vertices of the three squares are on the same line. What is the side
length of the smallest square?

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 A. 15
B. 16
C. 17
D. 18
E. 19

21 Two students, Geo and Har, are practicing algebra with two positive numbers A and B. Geo
takes the product of them and gets the number 12. Har takes the sum of the reciprocal (the
reciprocal of x is 1/x) of each number and also gets 12. What is A + B?

A. 7
B. 8
C. 13
D. 24
E. 144

22 The four vertices of the rectangle R1 are strictly inside (not on the sides of) another rectangle
R2 . Which of the following statements is NOT necessarily correct?

A. The R2 has larger area.

23 A(−3, −3), B(−1, 1), C(10, 10) and D(5, −5) are four points on the plane. For each point on
the plane compute the sum of the distances from that point to A, B, C and D. Which of the
following points has the smallest sum?

A. (0, 0)
B. (1, 1)
C. (2, 2)
D. (3, 3)
E. (4, 4)

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24 There are five positive integers. Their median is 2 larger than their mean and 10 larger than
their unique mode. What is the smallest possible range of the five numbers?

A. 14
B. 15
C. 16
D. 19
E. 20

25 How many ways are there to cover a 3-by-3 grid with four 1-by-2 dominoes and one unit square?
The following graphs are two such examples. Rotations are considered as different ways.

A. 16
B. 18
C. 20
D. 22
E. 24