Listen carefully. This accelerated course takes the AoPS Introduction series (Prealgebra, Introduction to Algebra, Introduction to Geometry), pairs them with Alcumus practice and AoPS videos, and demands relentless, daily work until mastery. You will not skim — you will solve. Every section in Rusczyk’s books begins with problems so you try first; that’s non-negotiable. Expect a minimum of 90–120 minutes of focused math on school days and 2–3 hours on weekends. Use the solutions manual only after an honest struggle of at least 20–30 minutes per problem. No calculator unless the problem explicitly allows one. Weekly structure: Monday–Thursday intensive problem sets from the current unit (target: 8–12 problems/day), Friday review & Alcumus adaptive practice, Saturday timed mixed-problem set (to simulate contest pressure), Sunday video lesson + writeup of solutions. Keep a single notebook for polished solutions — you will hand it in for review (or simulate review by self-checking against rigorous rubric). Record errors and categorize them: algebraic manipulation, conceptual, oversight. Reduce repeats to zero.
Unit plan (accelerated, one academic year compressed or intensive semester as desired). Prealgebra (3–5 weeks): arithmetic properties, exponents, primes/factorization, fractions, ratios, rates, percents, square roots, basic geometry (angles, perimeter, area) and introductory counting. Introduction to Algebra (8–12 weeks): linear equations/inequalities, systems, ratios and proportions in depth, quadratic equations and factoring, polynomials, functions, sequences, absolute value, complex numbers introduction, graphing lines and parabolas, exponents & logarithms overview. Discrete topics interleaved: divisibility, modular thinking, Pigeonhole Principle, foundational counting & basic probability. Each unit ends with a cumulative timed assessment and a problem set drawn from AoPS older contest collections. Weekly Alcumus targets: accuracy >90% and at least 25 new problems per week in the current topic; report progress to a mentor or parent.
Geometry (8–10 weeks intensive): similar triangles, congruence, polygons, circles (arcs, chords, tangents), power of a point, area strategies (including ‘funky’ areas), 3D solids, transformations, and introductory trigonometry (SOHCAHTOA for right triangles and trig ratios for contest-style proofs). Emphasize diagram accuracy, synthetic proofs, and multiple solution methods (coordinate, vector, synthetic). Integrate problem-solving strategies throughout: invariants, extreme principle, bounding, constructive methods. Assessment cadence: weekly small tests, biweekly mixed-topic NT/CP problems, monthly full-length mock AMC/AIME style set depending on target contest. By course end you must be able to: craft clear solutions, explain reasoning aloud, and solve novel problems under time pressure. If you fail to meet checkpoints, double daily practice until you do. This is not encouragement — it’s the plan. Follow it, and you will be prepared not just for class, but for national contests and deeper mathematical thinking.