The AMC 10 is one of the most respected mathematics competitions in the world for students in Grade 10 and below. It is the gateway to AIME, USAJMO, and ultimately the US International Mathematical Olympiad team. For Indian students targeting global STEM universities, a strong AMC 10 performance is a genuine differentiator on any academic profile.
But AMC 10 preparation is significantly different from preparing for school Maths or even standard Olympiad exams like IOQM. This complete guide covers the AMC 10 syllabus, important topics, scoring strategy, and a step-by-step preparation plan that actually works.
The AMC 10 is the entry point to the American Mathematics Olympiad pipeline: AMC 10 → AIME → USAJMO, and onward to national olympiad training programs. The contest itself is 25 multiple-choice questions in 75 minutes, drawn from the curriculum through Grade 10 — algebra, geometry, number theory, and counting and probability, with no trigonometry, logarithms, or complex numbers.
The AMC 10 is open to students in Grade 10 or below who are under 17.5 years of age on competition day. It is offered twice each November as the AMC 10A and AMC 10B — two different exams a week apart, not two sittings of the same test
Exam Dates:
| Competition | Date |
| AMC 10A and AMC 12A | 5 November 2026 |
| AMC 10B and AMC 12B | 13 November 2026 |
Complete Exam Pattern:
| Detail | Information |
| Total Questions | 25 |
| Duration | 75 minutes |
| Question Type | Multiple choice — 5 options (A to E) |
| Calculator | NOT allowed |
| Correct Answer | 6 points |
| Blank Answer | 1.5 points |
| Wrong Answer | 0 points |
| Maximum Score | 150 points |
| AIME Qualification | Score 100 or above |
Scoring Strategy Note: Leaving a question blank is worth a quarter of a correct answer, which means disciplined omission is a scoring strategy, not a concession. A student who answers 14 questions correctly and leaves the remaining 11 blank scores 100.5 and clears the AIME threshold.
The AMC 10 questions follow a difficulty distribution where questions 4 to 10 are must-know essential foundational math topics where students should achieve 50 to 70% accuracy.
| Questions | Difficulty | Target Accuracy |
| Q1 to Q10 | Easy to Medium | Should attempt all — under 1 minute each |
| Q11 to Q20 | Medium to Hard | Average 2 to 3 minutes each |
| Q21 to Q25 | Very Hard | Attempt only if time permits |
A student who reliably scores 18 out of 25 on the front and middle questions plus two of the last five hits the AIME cutoff in most years — far more achievable than trying to crack the last five reliably.
The AMC 10 is a 25-question, 75-minute multiple-choice competition. The content covers mathematical topics such as elementary algebra, basic geometry, area and volume formulas, elementary number theory, and elementary probability. Advanced topics like trigonometry, advanced algebra, and advanced geometry are excluded.
Here is the complete AMC 10 syllabus with detailed sub-topics:
Algebra is the language of the AMC 10 and typically makes up 40 to 50% of the exam.
| Sub-Topic | Key Concepts |
| Quadratic Equations | Vieta’s formulas, roots and coefficients, discriminant |
| Systems of Equations | Substitution, elimination, word problem application |
| Sequences | Arithmetic and geometric sequences, sum formulas |
| Functions | Domain, range, composition, function transformation |
| Inequalities | Absolute value inequalities, AM-GM inequality |
| Polynomials | Factoring techniques, polynomial manipulation |
| Word Problems | Rate, work, mixture and age problems |
| Simon’s Favorite Factoring Trick | Integer equations — SFFT applications |
For triangles, similar and congruent triangles appear everywhere in AMC 10. Students must know the properties of centroids, circumcenters, orthocenters, and incenters. For circles, the Power of a Point Theorem is essential — without it, circle problems take 10 minutes instead of 2.
| Sub-Topic | Key Concepts |
| Triangles | Similarity, congruence, area formulas, special triangles |
| Circles | Power of a Point, inscribed angles, tangent properties |
| Coordinate Geometry | Distance, midpoint, slope, equations of lines and circles |
| Quadrilaterals | Trapezoids, parallelograms, cyclic quadrilaterals |
| 3D Geometry | Volume and surface area of prisms, pyramids, spheres |
| Area Techniques | Shoelace formula, decomposition, ratio methods |
Number theory and counting are the highest-return topics for AMC 10 preparation because school curricula cover them the least, meaning improvement here is fastest with targeted practice.
| Sub-Topic | Key Concepts |
| Divisibility | GCD, LCM, divisibility rules |
| Prime Numbers | Prime factorization, number of divisors |
| Modular Arithmetic | Remainders, congruences, Euler’s Totient |
| Perfect Squares and Cubes | Pattern recognition in number problems |
| Digit Problems | Units digit, digit sum patterns |
| Diophantine Equations | Integer solution problems |
Combinatorics expands significantly from AMC 8 level in AMC 10. Students must master counting techniques, probability, and their applications in creative problem contexts.
| Sub-Topic | Key Concepts |
| Counting Principles | Multiplication rule, addition rule, casework |
| Permutations and Combinations | Arrangements, selections, circular permutations |
| Probability | Simple and compound events, conditional probability |
| Expected Value | Average outcome calculations |
| Pigeonhole Principle | Applications in combinatorial problems |
| Inclusion-Exclusion | Overcounting correction technique |
| Bijection | One-to-one correspondence counting |
Both AMC 10 and AMC 12 exams share several problems in the middle of each paper, but the AMC 12 leans harder into precalculus-level topics like trigonometry, logarithms, and complex numbers, while the AMC 10 stays within a geometry, algebra, counting, and number theory band.
| Aspect | AMC 10 | AMC 12 |
| Grade Eligibility | Grade 10 and below | Grade 12 and below |
| Age Limit | Under 17.5 years | Under 19.5 years |
| Trigonometry | Not included | Included |
| Logarithms | Not included | Included |
| Complex Numbers | Not included | Included |
| AIME Qualification | Score 100+ | Score 100+ |
| Difficulty | Moderate to Hard | Hard to Very Hard |
Recommendation for Indian students: If you are in Grade 9 or below, start with AMC 10. If you are strong in Algebra and Geometry and comfortable with pre-calculus topics, consider AMC 12 in Grade 11 or 12.
AMC 10 preparation follows three phases — building foundational math knowledge, developing pattern recognition and problem-solving flexibility, and peak preparation through timed full paper practice.
Phase 1 — Foundation Building (Months 1 to 3)
Begin with Art of Problem Solving Introduction series — Introduction to Algebra, Counting and Probability covers 95% of AMC 10 content at the right depth. Do not jump to advanced books yet.
What to do in Phase 1:
Spend a week doing only Triangle problems from the last 10 years of exams, then a week doing only Circle problems. This topic immersion approach builds the pattern recognition speed that AMC 10 demands.
What to do in Phase 2:
Simulate real test conditions at least 2 to 3 times per week in the last month before the exam. With 75 minutes and 25 questions, you get about 3 minutes per problem on average — the first 10 questions should take under 1 minute each.
What to do in Phase 3:
Two rules most students learn the hard way — easy problems matter as much as hard ones because both are worth 6 points whether the question is number 2 or number 22. And never trust the “almost have it” feeling — five minutes on a problem you will miss is 6 points of opportunity cost elsewhere.
How to apply the Skip Strategy:
| Aspect | AMC 10 | IOQM | JEE Maths |
| Conducted By | MAA — USA | MTA India | NTA India |
| Eligible Grades | Grade 10 and below | Class 8 to 12 | Class 11 to 12 |
| Format | 25 MCQ — 75 min | 30 integer — 3 hours | 30 MCQ — 60 min |
| Trigonometry | Not included | Included | Included |
| Calculator | Not allowed | Not allowed | Not allowed |
| Leads To | AIME → USAJMO | RMO → INMO → IMO | IIT and NIT Admission |
AMC 10 preparation builds Algebra, Geometry, and Number Theory skills that directly strengthen IOQM preparation and JEE Maths performance.
| Resource | Best For |
| AoPS Introduction to Algebra | Algebra foundation |
| AoPS Introduction to Counting and Probability | Combinatorics foundation |
| AoPS Introduction to Geometry | Geometry foundation |
| Past AMC 10 Papers (2010 to 2026) | Pattern recognition and timed practice |
| Art of Problem Solving Volume 1 | General competition problem solving |
At Ajay Sir Maths, our Olympiad coaching builds the exact mathematical reasoning AMC 10 demands. Ajay Sir personally teaches Number Theory, Algebra, and Combinatorics with complete individual attention — the same deep conceptual approach that makes complex AMC 10 problems feel logical and solvable.
Our Foundation course builds the strong Algebra and Geometry foundations that every AMC 10 student needs from Grade 6 onwards. Students preparing for both AMC 10 and JEE Maths find significant overlap in Algebra, Coordinate Geometry, and Number Theory — our coaching covers both curricula effectively.
Here is what our AMC 10 preparation coaching includes:
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The AMC 10 is a 25-question, 75-minute mathematics competition by the Mathematical Association of America for students in Grade 10 or below who are under 17.5 years old on exam day. It leads to AIME qualification for top scorers.
AMC 10 covers Algebra including quadratics, sequences and functions; Geometry including triangles and circles; Number Theory including primes and modular arithmetic; and Combinatorics including counting and probability. Trigonometry, logarithms, and calculus are not always included.
Students scoring 100 or above on AMC 10 qualify for AIME. A student who answers 14 questions correctly and leaves the rest blank scores 100.5 and clears the threshold always.
You can appear for both AMC 10A and AMC 10B in the same year, as they are different exams on different dates. Both use the same scoring system, and the AIME cutoff is always.
AMC 10 is significantly more difficult than AMC 8. It adds Intermediate Algebra, Coordinate Geometry, Number Theory depth, and Combinatorics — topics that go well beyond AMC 8 level.
Yes, Indian students can appear for AMC 10 through an approved MAA International testing center or school in India. Check the current MAA international arrangements before planning participation.
Long-term preparation starting in Grade 6 or 7 is ideal. For students starting in Grade 8 or 9, a focused 12-month preparation following the three-phase approach gives the best results always.
Author of DOOR TO IIT (A book of Mathematics for JEE (Mains +Advanced ) Preparation ) Teaching exp.11 year in most reputed coaching in India. Mentor of JEE top rank AIR-12,19, 28 & many more in top 100 in JEE Advanced. Many of students got 100%tile in JEE mains along with 100% marks in board exams.
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