admin A New 400-Page Training Resource for Learning, Practice, Strategy, and Competition Success
Mathematics competitions are not won by memorizing more formulas.
They are won by learning how to think mathematically.
How do you recognize the structure hidden inside an unfamiliar problem? How do you decide which method to try first? How do you know when a seemingly complicated problem has a surprisingly simple solution? How do you develop the speed and accuracy required to make good decisions under competition conditions?
These questions are at the heart of AMC 10 Mathematics: A Rigorous Guide to Mathematical Problem Solving, a new 400-page, 8.5 × 11 mathematics resource designed for students preparing for the AMC 10 and for students who want to build a strong foundation in higher-level competition mathematics.
The book is now available in Paperback and Hardcover editions through Amazon.
Why AMC 10 Matters
The American Mathematics Competitions (AMC), administered by the Mathematical Association of America, provide one of the most important pathways for developing mathematical problem-solving ability among middle and high school students.
The AMC 10 is a 25-question, 75-minute multiple-choice competition for students in grade 10 and below. Its problems emphasize areas such as algebra, geometry, number theory, probability, and other pre-calculus mathematics, while testing students through non-routine problems rather than routine classroom exercises.
But the importance of AMC 10 extends beyond a single examination.
For ambitious students, competition mathematics can become a long-term journey:
AMC 10 → AIME → higher-level mathematical competitions → Olympiad-level mathematics
The exact qualification rules and pathways can change from year to year, so students should always consult the current official MAA rules and announcements. Nevertheless, the underlying mathematical progression remains clear: strong performance in elementary competition mathematics can become the foundation for increasingly sophisticated mathematical problem solving.
That is the broader purpose behind this book.
More Than an AMC 10 Preparation Book
There are many ways to prepare for a mathematics competition.
One approach is to memorize formulas, collect tricks, and solve as many problems as possible.
Another approach is to develop a mathematical system that allows you to understand, organize, and solve unfamiliar problems.
AMC 10 Mathematics follows the second approach.
The goal is not simply to help students answer more questions.
The goal is to help them become better problem solvers.
The book brings together four central components:
Learn
Build a rigorous understanding of the mathematical ideas that repeatedly appear in competition problems.
Practice
Solve carefully selected problems that develop fluency, recognition, flexibility, and mathematical maturity.
Strategy
Learn how to approach unfamiliar problems, identify useful structures, manage time, test ideas, eliminate choices, and decide when a particular technique is appropriate.
Succeed
Bring knowledge, practice, and strategy together under realistic competition conditions.
The philosophy is simple:
Learn the ideas. Recognize the structure. Choose the strategy. Solve with confidence.
What Is Inside the Book?
At approximately 400 pages, the book is designed as a substantial training resource rather than a short collection of tips or a problem anthology.
It combines:
- Rigorous mathematical theory
- Concept-building explanations
- Worked examples
- Problem-solving techniques
- Advanced shortcuts and observations
- Topic-wise practice
- Mixed practice
- Challenging competition problems
- Logic and mathematical modeling
- Probability and expected value
- Combinatorics
- Number theory
- Algebra
- Geometry
- Strategic problem solving
- Full-length AMC 10-style simulations
- Hints and answer guidance
- Structured progression toward more demanding mathematics
The organization is intended to allow students to use the book in multiple ways.
A student beginning AMC 10 preparation can work systematically through the theory and foundational examples.
A more experienced student can use the practice sections to identify weaknesses.
An advanced student can focus on challenging problems, strategy, mixed sets, and timed simulations.
Teachers and coaches can also use individual sections as supplementary classroom or training material.
Building Mathematical Thinking
A central principle of the book is that competition mathematics should not be reduced to a collection of isolated tricks.
A useful technique is valuable because you understand why it works and when it applies.
For example, a student should not merely memorize that a certain algebraic manipulation is useful. The student should learn to recognize the structural features of a problem that suggest that manipulation.
Similarly, in geometry, the goal is not simply to accumulate formulas. Students should learn to recognize similarity, symmetry, ratios, cyclic structures, coordinates, transformations, and other patterns that can turn a difficult diagram into a manageable problem.
In combinatorics and probability, students need more than formulas. They need to learn how to model a situation correctly before attempting to calculate anything.
In number theory, divisibility, congruences, parity, factorization, and modular reasoning become tools for reducing seemingly complicated questions to manageable structures.
This emphasis on recognition and strategy is one of the central themes of the book.
From Learning to Practice
Knowing mathematics and being able to use mathematics are different skills.
A student may understand a chapter perfectly while still struggling with a new competition problem.
That is why the book places significant emphasis on practice.
The problems are intended to serve different purposes.
Some reinforce fundamental ideas.
Some require students to combine multiple concepts.
Some develop strategic recognition.
Others are deliberately challenging and require persistence, experimentation, and a willingness to reconsider an initial approach.
The progression is designed to move students gradually from:
Understanding → Application → Connection → Strategy → Independence
The objective is not simply to increase the number of problems a student can solve.
It is to increase the number of unfamiliar problems that a student can approach intelligently.
Strategy Under Competition Conditions
Mathematical knowledge is only part of competition performance.
The AMC 10 is a timed examination: students have 75 minutes for 25 multiple-choice questions.
That means competition success also requires decision-making.
Should you solve this problem immediately or return to it later?
Can the answer choices be used strategically?
Is there a faster method than the standard computation?
Can an estimate eliminate several choices?
Is the problem testing a familiar structure in an unfamiliar form?
When should you abandon an approach?
How should you allocate your remaining time?
These are mathematical and strategic questions at the same time.
The book therefore treats problem-solving strategy and competition strategy as skills that can be developed deliberately, rather than as abilities that students are simply expected to possess.
Preparing for the Next Level
AMC 10 preparation can also serve a much broader purpose.
Students who become comfortable with non-routine mathematical problems begin to develop habits that transfer naturally into more advanced competition mathematics.
They learn to:
- Look for patterns rather than immediately calculate.
- Break complicated problems into smaller structures.
- Search for invariants and constraints.
- Use multiple representations.
- Make educated conjectures.
- Test special cases.
- Work backward.
- Estimate before calculating exactly.
- Recognize when a standard technique is applicable.
- Persist when an immediate solution is not visible.
These habits form an important foundation for further study in competition mathematics.
For students who eventually aim toward AIME and higher-level Olympiad mathematics, the AMC 10 can therefore be viewed not merely as an isolated contest but as part of a longer mathematical development pathway.
The MAA currently describes AMC 10 as providing a first step toward the USA’s pathway into prestigious international mathematics competitions, including the International Mathematical Olympiad.
The purpose of this book is to help students build the mathematical foundation needed to take that next step.
Designed for Serious Students of Mathematics
This book is particularly suited to students who want more than routine textbook exercises.
It is intended for:
Students preparing for AMC 10
Students looking for a structured and rigorous preparation resource covering concepts, practice, strategy, and timed competition work.
Students interested in competition mathematics
Students who enjoy challenging problems and want to develop mathematical reasoning beyond the standard school curriculum.
Students preparing for future AIME-level mathematics
Students who want to strengthen their foundations before moving toward more demanding competition problems.
Teachers and mathematics coaches
Educators looking for a substantial collection of concepts, examples, strategies, and practice material for structured competition training.
Parents supporting advanced mathematics education
Parents looking for a serious resource that develops mathematical thinking rather than simply providing repetitive exercises.
A Second Edition Built for Deeper Training
This is the Second Edition of the book.
The new edition has been developed with an emphasis on improving the overall training experience: stronger conceptual explanations, expanded practice, more rigorous problem-solving development, improved strategic guidance, and a broader progression from foundational ideas toward challenging competition mathematics.
The intention is not simply to make the book longer.
It is to make the training system better organized, more rigorous, and more useful.
Every section should contribute to the larger objective:
Develop the ability to solve unfamiliar mathematical problems.
A Large-Format 400-Page Resource
The book is published in an 8.5 × 11 inch format with approximately 400 pages.
The large format provides sufficient space for mathematical notation, diagrams, worked solutions, examples, exercises, and practice sets without compressing the material into an unnecessarily dense layout.
It is designed to function as a serious reference and training book that students can return to repeatedly during their AMC 10 preparation.
Paperback and Hardcover Editions
The book is currently available in two physical editions on Amazon.com:
Paperback
US $39.99
Approximately 400 pages
8.5 × 11 inch format
Hardcover
US $59.99
Approximately 400 pages
8.5 × 11 inch format
The Hardcover edition is intended for students, families, teachers, and mathematics enthusiasts who prefer a more durable long-term reference copy.
Where to Buy
The book is available through Amazon marketplaces in several countries.
United States
Amazon.com — US $39.99 Paperback / US $59.99 Hardcover
Canada
Germany
Australia
France
Singapore
For other countries, search for the book by its title or ISBN/ASIN on your local Amazon marketplace.
Begin the Journey
Competition mathematics is a journey.
The first goal may be to understand the mathematics.
The next is to solve unfamiliar problems.
Then comes the ability to solve them efficiently.
Eventually, the goal becomes something deeper: to look at a problem and see the mathematical structure that lies beneath it.
That development does not happen overnight.
It comes through deliberate study, thoughtful practice, reflection, and persistence.
AMC 10 Mathematics: A Rigorous Guide to Mathematical Problem Solving is designed to support that journey.
Whether your immediate goal is to prepare for the next AMC 10, strengthen your mathematical foundation, or begin a longer journey toward advanced competition mathematics and Olympiad-level problem solving, the work begins with the same fundamental question:
Can you learn to think differently about a problem?
This book is an invitation to begin.
Learn. Practice. Strategize. Solve.
And keep going.
About the Author
Rishabh Kumar is a mathematics educator and author focused on rigorous mathematical learning, competition mathematics, and problem solving. His work emphasizes conceptual understanding, strategic thinking, and developing the ability to approach unfamiliar mathematical problems with confidence.
He is also developing a broader collection of mathematics resources designed to help students progress from strong mathematical foundations to advanced competition and Olympiad-level problem solving.
