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AMC 10 Mathematics is a rigorous, comprehensive guide to mathematical problem solving for students preparing for the American Mathematics Competitions (AMC 10) and for anyone seeking to develop stronger mathematical thinking. Designed around the ideas, techniques, and problem-solving habits that matter most in competition mathematics, this second edition goes beyond routine formula-based preparation. It develops concepts systematically, illustrates them through carefully chosen worked examples, and provides extensive practice that progresses from foundational techniques to challenging contest-style problems. The book covers the major areas of AMC 10 mathematics, including: • Algebra and equations Throughout the book, emphasis is placed on recognizing structure, choosing efficient methods, avoiding common traps, and developing solutions that are both accurate and elegant. The book includes: • Rigorous theory and essential concepts This is not intended to be merely a collection of formulas or tricks. The goal is to help students understand why methods work, recognize when to use them, and become increasingly independent problem solvers. The second edition has been substantially revised and expanded, with improved explanations, additional practice, upgraded problem-solving strategies, and a stronger emphasis on rigorous mathematical thinking. Whether used for structured preparation, independent study, classroom instruction, or long-term mathematical training, AMC 10 Mathematics is designed to serve as a complete foundation for serious competition-mathematics preparation.
• Functions and sequences
• Counting and combinatorics
• Probability and expected value
• Number theory
• Geometry
• Coordinate geometry
• Mathematical logic and modeling
• Strategic problem solving
• Worked examples with detailed reasoning
• Problem-solving strategies and advanced techniques
• Topic-based practice sets
• Challenging mixed problems
• Full-length AMC 10-style simulations
• Hints, answers, and solution guidance
• A structured progression from core skills to advanced problem solving
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