Imagine math as a series of rich, layered recipes — warm, precise, and infinitely rewarding. For a motivated 15-year-old, this accelerated 9–12 month plan combines the AoPS Introduction series with Alcumus practice and the free AoPS videos in a delicious, disciplined cadence.
- Months 1–3 — Solidify Foundations (Prealgebra): Begin with Prealgebra. Taste the basics: arithmetic properties, fractions, decimals, exponents, primes, ratios, rates, percents, square roots, and introductory geometry. Follow each section’s problems-first approach, then read solutions to learn techniques. Weekly: 6–8 hours; finish book problems and corresponding Alcumus modules.
- Months 4–7 — Deepen Algebra (Introduction to Algebra): Move to Introduction to Algebra. Focus on linear equations, inequalities, quadratic equations, factorization, functions, polynomials, sequences. Alternate textbook problem sets with Alcumus topic practice. Weekly: 8–10 hours; aim to master problem types and start timed problem sets.
- Months 8–10 — Explore Geometry (Introduction to Geometry): Savor geometry: similar and congruent triangles, circles, power of a point, polygons, 3D shapes, transformations, intro trig. Emphasize diagrams, synthetic proofs, and creative problem solving. Weekly: 7–9 hours, plus geometry Alcumus sets.
- Ongoing — Discrete Math, Counting & Number Theory: Sprinkle counting, probability, and number theory across the year. These chapters enhance contest-style thinking and appear in each book.
- Assessment & Practice: Monthly mock exams, track Alcumus progress, and use the solutions manuals for in-depth feedback. Revisit weak topics in focused 2-week cycles.
Final note: savor the process. Each problem is a small, indulgent challenge — chew it slowly, learn from the solutions, and delight in the elegant results.