AMC 12 Preparation Books
The AoPS Book Series (Ranked by Importance)
To solidify your foundational knowledge, it is highly recommended that you read the AoPS Introductory series of books. They are extremely comprehensive, though they require a significant amount of time to complete.
a. Introduction to Counting & Probability
b. Introduction to Geometry
c. Introduction to Algebra
d. Introduction to Number Theory
"the Art of Problem Solving, Volume 2: and Beyond"
*The Art of Problem Solving, Volume 2* is a classic problem-solving textbook used by many successful high school math teams and enrichment programs. Volume 2 is suitable for students who have already mastered the fundamentals introduced in Volume 1 and are ready to tackle greater challenges. Far more than just a collection of techniques, this book emphasizes learning and understanding methodologies rather than memorizing formulas, thereby enabling students to apply what they have learned to solve a wide range of problems.
AoPS Intermediate Series Books
a. Intermediate Algebra
b. Intermediate Counting & Probability
PreCalculus by AoPS (Chapters 1-8)
It contains nearly 1,000 problems, ranging from routine exercises to highly challenging problems drawn from major mathematics competitions.
Mastering AMC 10/12
This book will help you learn and practice advanced concepts useful for AMC 10 problems, such as Linearity of Expectation, Markov Chains, Cyclic Quadrilaterals, and more.
An Essential Resource for AMC 12 Prep — 4 Textbooks + 2 Workbooks!
This AMC 12 study set consists of 6 volumes (5 core textbooks + 1 workbook), designed specifically for students preparing for the AMC 12 competition.
Featuring 4 textbooks and 2 expertly curated workbooks, this set creates a seamless study-and-practice loop that doubles your learning efficiency!
Comprehensive Coverage from Fundamentals to Advanced Mastery: Guiding you step-by-step—from basic concepts and high-frequency competition challenges to advanced problem-solving strategies—to help you reach the pinnacle of competitive math success!
1,000+ Problems with Detailed Solutions: Every problem includes a standard answer accompanied by a step-by-step breakdown of the solution process, enabling you to instantly crack even the most tricky and complex problem types!
The AMC 12 preparation books listed above have been bundled and organized!
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A List of Resources for Preparing for the AMC 12
Step I:
If you are new to math competitions or are taking the AMC 12 for the first time, you need to ensure that you have a solid understanding of fundamental mathematical concepts. You can use the following resources to get started:
1. AMC 10/12 Fundamentals Course: A free course covering the most basic concepts for the AMC 10/12, such as Expected Value, Modular Arithmetic, Diophantine Equations, Power of a Point, and more.
2. AoPS Volume 1: This volume primarily serves as a summary of the AoPS Introduction series, covering a wide range of important concepts.
Step II (If time permits)
To consolidate your foundational knowledge, it is highly recommended that you read the AoPS Introduction series books. They are quite comprehensive, but they take a significant amount of time to complete.
You can also use Alcumus and these books for additional practice.
Additionally, you can check out paid courses from AlphaStar Academy, Art of Problem Solving, and many other organizations.
Step III
During the final 1–2 months leading up to the competition, it is crucial to review and refresh all key concepts relevant to the AMC 12 exam.
Volume 2 (Book by AoPS)
Volume 2 is designed for students who have already mastered the problem-solving fundamentals introduced in Volume 1 and are ready to tackle greater challenges.
Intermediate Series (Books by AoPS)
a. Intermediate Algebra
b. Intermediate Counting & Probability
Precalculus (Book by AoPS — Chapters 1–8)
This Precalculus course covers trigonometry, complex numbers, vectors, and matrices. It features nearly 1,000 problems, ranging from routine exercises to highly challenging questions drawn from major mathematics competitions.
*Mastering AMC 10/12*: This book will help you learn and practice advanced concepts useful for solving AMC 10 problems.
Step 4
List of Mock Competitions
1. Official AMC 12 Solutions from Previous Years: Use these tests, administered with a 75-minute timer, to simulate actual exam conditions. The difficulty of the AMC increases every year; therefore, only AMC 12 competitions from the fall of 2021 onwards truly represent the current difficulty level of the AMC 12.
2. AoPS-Created AMC 12 Mock Competition (2023): A high-quality mock competition created by problem writers from the Art of Problem Solving.
3. AoPS-Created AMC 12 Mock Competition (2022): A high-quality mock competition created by problem writers from the Art of Problem Solving.
4. AoPS-Created AMC 12 Mock Competition (2021): Another high-quality mock competition created by problem writers from the Art of Problem Solving.
5. User-Created AMC 12 Mock Competitions: These mock competitions are created by users on the AoPS forums; their quality and difficulty levels vary. However, if you have already completed all the official AMC 12 competitions from previous years, these still serve as excellent practice material.
7. CMC Mock Competitions: Almost every test created by the CMC—even those dating back to 2017—is of extremely high quality, with a difficulty level comparable to that of the current AMC exams.
Practice Math Problems
For additional practice, several useful websites are available to help you hone your skills in specific topics and improve your problem-solving speed.
1. Alcumus: A free resource provided by AoPS designed for practicing problems related to specific mathematical topics.
2. AMC Trivial: This website generates practice problems drawn from past competitions. You can even create custom mock exams based on historical questions, allowing you to focus on specific topics or difficulty levels.
3. MAATester: This website makes it easy to search for problems related to any specific topic across a wide variety of math competitions.
4. Winning: Practice your speed and accuracy by answering questions quickly while competing head-to-head against other players.
5. Math Llmlab: Take AMC exams in a digital format, or practice problems specifically related to particular mathematical concepts.
There are numerous YouTube videos covering skills that will prove helpful when taking the AMC—such as the instructional videos found in this playlist. This serves as a fantastic free resource for students seeking relevant study materials.
By utilizing these resources and practicing regularly, you can enhance your skills and significantly increase your chances of success on the AMC 12.
The AMC 12 Preparation Resource Package is now ready.
Scan the QR code to connect with an advisor, schedule an assessment and a 1-on-1 competition planning session, and receive a customized package of past exam questions. ⇓
