AMC 8 Past Problems with Detailed Solutions (2018-2024)

Introduction

The AMC 8 (American Mathematics Competition 8) is the world’s most prestigious and influential middle school mathematics competition, hosted annually by the Mathematical Association of America (MAA). Open to students in grade 8 and below (under 14.5 years old), it serves as the critical first stepping stone for students aiming to advance to the AMC 10/12, AIME, and ultimately the International Mathematical Olympiad (IMO).

Working through official past exams is the single most efficient way to improve your AMC 8 score: it lets you master the exam format, internalize core test topics, perfect your pacing for the 40-minute time limit, and identify critical gaps in your math knowledge.

On this page, we provided a centralized, structured resource for all official AMC 8 past papers, answer keys, and solution guides from 2018 to 2024. Whether you’re just starting your study plan, taking timed mock exams, or targeting last-minute score gains, this collection delivers end-to-end support for your AMC 8 journey.

Important Note: The 2021 AMC 8 examination was canceled globally due to the COVID-19 pandemic, so no official standard exam content is included for this year.

2024 AMC 8 Problems & Official Detailed Solutions

Difficulty Rating: ⭐⭐⭐⭐☆ (4.5/5) Best For: Advanced students targeting 18+ scores, final pre-exam mock tests, and mastering high-difficulty problem-solving logic

The 39th annual AMC 8 was held January 18–24, 2024. Aligned with recent exam trends, algebra and geometry problems made up over 60% of the test, while combinatorics questions emphasized logical reasoning and probability calculation, with elevated demands on problem-solving speed and critical thinking.

2024 AMC 8 Official Answer Key

High-Yield Hard Problem Breakdowns

Problem 20 (Core Geometry Test Point)

Key Solution: For an equilateral triangle formed by a cube’s vertices, all sides must be equal-length face diagonals (√2 for a side-1 cube). From vertex P, 3 valid face diagonals can be drawn, and any 2 form a unique equilateral triangle. Total: C(3,2)=3, answer D.

Problem 25 (Core Combinatorics & Probability Test Point)

Key Solution: Use complementary counting. Total ways to seat 8 passengers: C(12,8)=495. Invalid arrangements (no adjacent seats available) total 195. Valid probability: 1-195/495=20/33, answer C.

2023 AMC 8 Problems & Official Detailed Solutions

Difficulty Rating: ⭐⭐⭐⭐☆ (4.5/5) Best For: Students with a 15–20 baseline score looking to advance, real-world application practice, and realistic mock testing

The 38th annual AMC 8 was held January 17–23, 2023. This exam emphasized real-world scenario integration with mathematical concepts, with a slight increase in number theory problem weight. Its difficulty matches the 2024 exam closely, making it ideal for authentic mock test practice.

2023 AMC 8 Official Answer Key

High-Yield Hard Problem Breakdowns

Problem 22 (Core Number Theory Test Point)

Key Solution: Let the first two terms be a and b. The 6th term is a³b⁵=4000=2⁵×5³. Matching prime exponents gives a=5, b=2, answer D.

Problem 24 (Core Geometry Test Point)

Key Solution: Use the similar triangle area ratio rule (area ratio = square of corresponding height ratio). Set up the equation 1-(11/h)²=(h-5/h)², solve to get h=14.6, answer A.

2022 AMC 8 Problems & Official Detailed Solutions

Difficulty Rating: ⭐⭐⭐☆☆ (3.5/5) Best For: Beginner to intermediate students, early-stage preparation, and mastering core foundational test points

The 37th annual AMC 8 was held January 18–24, 2022, marking the first return to regular in-person exams post-pandemic. The test returned to classic, core AMC 8 topics, with a focus on flexible application of basic math knowledge — perfect for students just starting their AMC 8 preparation.

2022 AMC 8 Official Answer Key

High-Yield Hard Problem Breakdowns

Problem 23 (Core Combinatorial Counting Test Point)

Key Solution: Count valid configurations with at least one full row of △s and one full row of ○s (42 total), plus valid column-only configurations (42 total, no overlap with row cases). Total: 84, answer D.

Problem 25 (Core Probability Test Point)

Key Solution: Use recursive probability. Let pₙ = probability of returning to the start after n jumps. With p₀=1 and pₙ=1/3(1-pₙ₋₁), calculate to get p₄=7/27, answer E.

2020 AMC 8 Problems & Official Detailed Solutions

Difficulty Rating: ⭐⭐⭐⭐☆ (4.5/5) Best For: Students building innovative problem-solving skills, advanced practice, and logical reasoning training

The 36th annual AMC 8 was held November 10–16, 2020. This exam was highly innovative, with new number pattern and logical reasoning problem types that pushed students’ creative mathematical thinking. It’s ideal for students looking to go beyond basic practice and build advanced problem-solving skills.

2020 AMC 8 Official Answer Key

High-Yield Hard Problem Breakdowns

Problem 22 (Core Number Pattern Test Point)

Key Solution: Work backwards from the final output of 1. After 6 operations, valid initial numbers are 1, 8, 10, and 64. Their sum is 83, answer E.

Problem 23 (Core Permutation & Combination Test Point)

Key Solution: Split into two valid distribution cases: 3-1-1 (60 ways) and 2-2-1 (90 ways). Total valid distributions: 150, answer B.

2019 AMC 8 Problems & Official Detailed Solutions

Difficulty Rating: ⭐⭐⭐☆☆ (3.5/5) Best For: Foundational mock tests, core topic mastery checks, and mid-stage preparation progress tracking

The 35th annual AMC 8 was held November 12–18, 2019. With moderate difficulty and comprehensive coverage of all core AMC 8 test points, this is a classic benchmark exam for foundational preparation, perfect for testing your mastery of key topics.

2019 AMC 8 Official Answer Key

High-Yield Hard Problem Breakdowns

Problem 19 (Core Competition Logic Test Point)

Key Solution: 6 teams play 30 total games (max 90 total points). The top 3 teams can earn a maximum of 72 combined points, for a maximum per-team score of 24, answer C.

Problem 24 (Core Geometry Area Test Point)

Key Solution: Use similar triangles and area ratio rules to find BF:FG:GC=1:1:2. Calculate the area of △EBF as 30, answer B.

2018 AMC 8 Problems & Official Detailed Solutions

Difficulty Rating: ⭐⭐⭐☆☆ (3/5)

Best For: First-time test-takers, introductory AMC 8 practice, and building core exam familiarity

The 34th annual AMC 8 was held November 13, 2018. This is the classic benchmark paper for modern AMC 8 exams, with an even distribution of test points and a gentle difficulty gradient for hard problems. It’s the must-solve starting paper for all new AMC 8 test-takers.

2018 AMC 8 Official Answer Key

High-Yield Hard Problem Breakdowns

Problem 18 (Core Number Theory Test Point)

Key Solution: Prime factorization of 23232 is 2⁶×3¹×11². Use the divisor count formula: (6+1)(1+1)(2+1)=42, answer E.

Problem 24 (Core Solid Geometry Test Point)

Key Solution: The cross section is a rhombus with diagonals equal to the cube’s space diagonal (s√3) and face diagonal (s√2). Calculate the area ratio R=√6/2, so R²=3/2, answer C.

4-Step Guide to Efficient AMC 8 Preparation With Past Papers

Working through past papers is not just about solving problems — a scientific approach can 3x your preparation efficiency. This streamlined guide is tailored to the AMC 8’s format and requirements:

1. Foundation Phase (3–6 Months Pre-Exam): Topic-Specific Practice

Skip full mock tests at the start. Use our year-specific subpages to sort problems by the 4 core topics (algebra, geometry, number theory, combinatorics) and master one module at a time before moving on.

2. Intensive Phase (1–3 Months Pre-Exam): Timed Full Mock Tests

The AMC 8 gives you just 40 minutes for 25 problems (average 1m36s per question). Strict timed practice is non-negotiable: simulate the real exam environment, no notes or pauses, and track both your score and problems that took too long to solve.

3. Critical Review Step (After Every Mock Exam)

Wrong answers are more valuable than new ones. Categorize mistakes into 3 types:

• Knowledge gaps: Relearn the topic and practice 5 similar problems
• Careless errors: Log in an error notebook for pre-exam review
• Slow problem-solving: Learn shortcut methods (complementary counting, ratio method) to boost speed

4. Final Sprint Phase (1 Month Pre-Exam): Second Pass & Error Review

Re-solve the past 5 years’ papers, focusing on your wrong answers and high-yield hard problems. Maintain 1 mock test per week to keep your pacing, and avoid cramming new, untested content right before the exam.

AMC 8 Core Test Points & High-Frequency Problem Type Summary

The AMC 8 aligns with U.S. 7th and 8th grade math curriculum standards, with 4 core knowledge modules. This summary helps you prioritize your study:

Frequently Asked Questions (FAQ) About the AMC 8 Exam

Conclusion

The core of the AMC 8 exam is not testing complex formulas or rote calculation — it evaluates your mathematical thinking, logical reasoning, and flexible problem-solving skills. Official past papers are the single most valuable resource for mastering the exam’s patterns and maximizing your score.

If your goal is to score 20+ on the AMC 8, practicing past problems is only the first step. What really makes the difference is learning the patterns behind high-frequency problems and developing fast-solving strategies. At WuKong Math, our instructors help students break down AMC 8 problems into repeatable solving frameworks — not just answers. Book a free trial class and get a personalized AMC 8 preparation plan now!

Copyright Disclaimer: All AMC 8 problems and content are the sole property of the Mathematical Association of America (MAA). This page provides educational summaries, official answer keys, and instructional explanations only for non-commercial exam preparation purposes.

Demi | WuKong Math Teacher

I am an educator from Yale University with ten years of experience in this field. I believe that with my professional knowledge and teaching skills, I will be able to contribute to the development of Wukong Education. I will share the psychology of children’s education and learning strategies in this community, hoping to provide quality learning resources for more children.