Newton Olympiad Academy
COURSEWARE FOR AMC 10 AND 12 PATHWAY
| SESSION | TOPIC | 45-MINUTE CONCEPT PORTION | 45-MINUTE PROBLEM SOLVING PORTION | ASSIGNMENT FOCUS |
|---|---|---|---|---|
| 1 | Foundations of Olympiad Problem Solving | AMC structure, mathematical thinking, pattern recognition, logical deduction, estimation, working backwards | Introductory AMC strategy problems, logical puzzles, elimination methods | Pattern recognition drills, beginner AMC worksheet |
| 2 | Algebra Essentials I | Linear equations, quadratics, factoring, Vieta’s formulas, polynomial identities | Functional equations, substitutions, hidden factorization | Algebra drills, polynomial challenge problems |
| 3 | Algebra Essentials II | Inequalities, AM-GM, Cauchy basics, absolute value, systems of equations | Olympiad inequalities, symmetric systems, substitution techniques | Inequality worksheet, advanced algebra set |
| 4 | Sequences & Functional Thinking | Arithmetic & geometric sequences, recursion, functional equations basics | Recursive reasoning, pattern generation, functional substitutions | Sequence challenges, recursion practice |
| 5 | Number Theory I | Divisibility, primes, modular arithmetic, remainders, congruences | Last digit problems, cyclicity, modular reasoning | Modular arithmetic worksheet, prime challenges |
| 6 | Number Theory II | Diophantine equations, GCD & LCM, Euclidean algorithm, bases | Integer solution strategies, divisibility arguments | Integer problem set, advanced number theory |
| 7 | Counting & Combinatorics I | Counting principles, permutations, combinations, complement counting | Arrangement problems, restrictions, casework | Counting drills, combinatorics worksheet |
| 8 | Counting & Probability II | Probability basics, expected value intuition, Pascal’s triangle, binomial concepts | Probability traps, combinatorial probability, advanced counting | Probability challenge sheet |
| 9 | Geometry Essentials I | Angles, triangles, similarity, congruence, circles basics | Angle chasing, hidden geometry, visual reasoning | Geometry, workbook, diagram exercises |
| 10 | Geometry Essentials II | Coordinate geometry, distance formula, midpoint theorem, circle equations | Coordinate transformations, graph-based geometry | Coordinate geometry worksheet |
| 11 | Advanced Geometry & Trigonometry | Trigonometric identities, sine rule, cosine rule, area relations | Trigonometric simplifications, geometry proofs | Trigonometry drills, olympiad geometry |
| 12 | Advanced Algebra & Polynomials | Higher-degree polynomials, symmetric expressions, rational root theorem | Polynomial manipulation, root analysis | Advanced polynomial worksheet |
| 13 | Advanced Problem Solving Strategies | Invariants, extremal principle, pigeonhole principle, constructive methods | Multi-topic olympiad problems, strategy selection | Olympiad strategy worksheet |
| 14 | Speed Mathematics & Exam Techniques | Time management, elimination methods, mental math shortcuts, smart guessing | Timed AMC drills, error analysis | Timed speed practice problems |
| 15 | Integrated Olympiad Workshop | Multi-topic synthesis, advanced reasoning, AIME introduction | Integrated AMC challenge problems, discussion-based solving | Final enrichment worksheet |
