2024
2024 AMC8 Paper & Solutions Pick
12 selected sample solutions with difficulty tags and topic distribution. Features: 3D unfolding, circular arrangements.
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12 Sample Questions
40 Minutes
Max Score 25
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Exam Overview
Exam Overview
This exam emphasizes multiple math topics. Overall difficulty is moderate.
Difficulty
- EasyQ1-10
- MediumQ11-20
- HardQ21-25
Topics
- Algebra35%
- Geometry35%
- Number Theory15%
- Combinatorics15%
Awards
Distinguished Honor Roll
Distinguished Honor Roll (Top 1%)
21+
Honor Roll
Honor Roll (Top 5%)
18+
Achievement Roll
Grade 6 and below · 15+ points
15+
Sample Problems
2024 AMC8 Sample Problems (12 questions)
Sample reference problems by difficulty — click an option to check your answer
Q1EasyFour arithmetic operations
Calculate the value of (15 + 7) × 3 - 24 ÷ 6.
Steps
Do multiplication and division before addition and subtraction: 22 × 3 - 4 = 66 - 4 = 62
Answer: EWatch the order of operations: parentheses first, then multiplication and division, and finally addition and subtraction
Q3EasyKey concept: fractions
If 2/3 of a number equals 18, what is 1/4 of that number?
Steps
2x/3 = 18 → x = 27
x/4 = 27/4 = 6.75
Answer: BUse division to reverse the operation
Q6EasyConvert percentages to fractions
A piece of clothing originally costs 200 yuan. Its price is first reduced by 20% and then increased by 25%. What is the final price?
Steps
Decrease by 20%: 200 × 0.8 = 160
Increase by 25%: 160 × 1.25 = 200
Final = original price
Answer: BDecreasing first and then increasing does not necessarily return to the original price; it depends on the specific percentages
Q9EasyApply the relevant mathematical concept
What is the sum of the median and the mode of the data 3, 5, 7, 5, 10?
Steps
Sort: 3, 5, 5, 7, 10
Median = 5 (the middle value), mode = 5 (occurs most often)
Sum = 5 + 5 = 10
Answer: CThe median is the middle value after sorting; the mode is the most frequent value
Q11MediumKey concept: functions
Given f(x) = 3x - 1, find the value of f(f(2)).
Steps
f(2) = 3(2) - 1 = 5
f(f(2)) = f(5) = 3(5) - 1 = 14
Answer: CEvaluate a composite function from the inside out, one layer at a time
Q14MediumArea
A parallelogram has a base of 12 and a height of 8. After drawing a diagonal, what is the area of one of the triangles?
Steps
Area of the parallelogram = 12 × 8 = 96
The diagonal divides it into two triangles of equal area
Area of one triangle = 96/2 = 48
Answer: AA diagonal bisects the area of a parallelogram
Q16MediumPrime Factorization
When 168 is factored into prime factors, what is the sum of all its distinct prime factors?
Steps
168 = 2³ × 3 × 7
Distinct prime factors: 2, 3, 7
Sum = 2 + 3 + 7 = 12
Answer: EBe careful to distinguish "distinct prime factors" from "prime factors counted with repetition"
Q18MediumSpatial reasoning
A cube has its six faces labeled 1-6, with 1 opposite 6, 2 opposite 5, and 3 opposite 4. Face 1 is placed face-down on a table. After rolling the cube forward once, which face is now on top?
Steps
Face 1 is on the bottom → face 6 is on top (opposite face)
Roll forward: the top face → the front, the back face → the top
Face 6 moves to the front, and the original back face (face 3) moves to the top
The face on top = 3
Answer: AWhen rolling a cube, track the position of each face step by step
Q21HardNumber of factors = product of (exponent+1)
How many positive integers from 1 to 2000 are perfect squares with exactly 3 positive divisors?
Steps
Exactly 3 divisors → of the form p² (where p is prime)
p² ≤ 2000 → p ≤ 44
Primes up to 44: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43
14 in total
Answer: ADivisor-count formula: n = p^a → number of divisors = a + 1
Q22HardComprehensive equation
Person A has 3 times as much money as person B. After A gives B 20 yuan, A has 80 yuan more than B. How much money did A have originally?
Steps
Let B originally have x yuan, so A originally has 3x yuan
After A gives B 20: A = 3x − 20, B = x + 20
(3x − 20) − (x + 20) = 80 → 2x − 40 = 80 → x = 60
A = 3 × 60 = 180
Answer: C"Giving" means one side loses what the other gains, so both amounts change
Q24HardKey concept: permutations
Five people stand in a row, and A and B must be next to each other. How many arrangements are there?
Steps
Bundle A and B together as a single unit: 4! = 24
A and B can switch places within the unit: ×2
Total arrangements = 24 × 2 = 48
Answer: BFor adjacency problems, use the "bundling method"
Q25HardGeometry
A square inscribed in a circle has an area of 50. Find the area of the circle (use π ≈ 3.14).
Steps
Area of the square = 50 → side length = √50
Diagonal = side length × √2 = √100 = 10
Diagonal = diameter of the circle → radius = 5
Area of the circle = π × 25 ≈ 78.5
Answer: AThe diagonal of a square inscribed in a circle equals the circle's diameter
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